Regression Analysis — Class 11 Applied Maths Complete Guide | Boundless Maths
Syllabus 6.4 Part of Unit 5 CBSE 2026–27 Not Yet in Most Textbooks

Regression Analysis
— The Complete Guide

CBSE Class 11 Applied Mathematics · Unit 5, Topic 6.4 · Concept, Properties, Worked Examples & Practice

Regression Analysis is a newly added syllabus topic with very little textbook coverage so far. This page gives you everything: the concept, how it differs from correlation, regression equations and coefficients, 6 key properties, 20 fully worked examples, practice MCQs and exam tips — all free, all in one place.

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Key Properties
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Core Formulas
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MCQs + AR
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Short Answers
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Long Answers

Regression Analysis for Class 11 Applied Maths — Why This Page Exists

Regression Analysis was added to the CBSE Class 11 Applied Mathematics syllabus (topic 6.4, under Unit 5: Descriptive Statistics) but most published textbooks haven't caught up yet — students are often left without clear explanations or solved examples. This page closes that gap: a complete, exam-ready guide covering the concept, how it differs from correlation, the regression coefficients and equations, six essential properties, and 20 fully worked examples.

Regression Coefficients Y on X & X on Y 6 Key Properties 20 Worked Examples
Start Here

What Is Regression Analysis?

The mathematical tool for prediction — not just measuring relationships, but using them.

Regression analysis is a statistical method used to establish a mathematical relationship between two or more variables, so that the value of one variable can be predicted from the known value of another.

The word regression literally means "to go back." It was introduced by Sir Francis Galton, who observed that tall fathers tend to have sons shorter than themselves — the sons' heights "regressed" toward the average height of the population.

💡 Key Idea

While correlation tells us whether and how strongly two variables are related, regression tells us exactly how one variable changes with respect to another — and allows actual prediction.

The Simple Analogy

Imagine you notice that taller people tend to weigh more.

Correlation asks:

"How strongly are height and weight related?"

→ Gives you a number: r = 0.85

Regression asks:

"If someone is 170 cm tall, exactly how much do they weigh?"

→ Gives an equation: Weight = 0.9×Height − 52

Dependent & Independent Variables

In regression, we identify two roles for the variables:

  • Independent Variable (X): the variable that is known or controlled. Also called the predictor or explanatory variable.
  • Dependent Variable (Y): the variable whose value we want to predict. Also called the response variable.
Independent Variable (X)Dependent Variable (Y)
Hours studiedMarks scored
Advertisement expenditureSales revenue
Age of machineMaintenance cost
RainfallCrop yield
Side by Side

Regression vs Correlation — Are They the Same?

Short answer: No, they are NOT the same — but they are deeply connected. Think of them as two sides of the same coin.

FeatureCorrelationRegression
GoalMeasure the strength of relationshipPredict one variable from another
OutputA single number: r (between −1 and +1)An equation: Y = a + bX
DirectionShows + or − relationshipShows exact rate of change
Symmetric?Yes — r(X,Y) = r(Y,X)No — line of Y on X ≠ line of X on Y
Cause-Effect?No — just associationYes — one variable depends on another
How many results?1 value of r2 lines (Y on X, and X on Y)

Are the Formulas the Same? No — But They Share One Component

Here's where it gets interesting. Look at all three formulas:

Correlation

r = nΣXY − ΣX·ΣY√([nΣX²−(ΣX)²][nΣY²−(ΣY)²])

Regression coeff. (Y on X)

bYX = nΣXY − ΣX·ΣYnΣX² − (ΣX)²

Regression coeff. (X on Y)

bXY = nΣXY − ΣX·ΣYnΣY² − (ΣY)²

👉 Notice: The numerator is identical in all three formulas — nΣXY − ΣX·ΣY. The difference is only in the denominator:

  • r uses the square root of both denominators multiplied together
  • bYX uses only the X-denominator
  • bXY uses only the Y-denominator
r = ±√(bYX × bXY)

The correlation coefficient is literally the geometric mean of the two regression coefficients!

A Numerical Example to See the Difference Clearly

Suppose from data you calculate: bYX = 0.8 (regression of Y on X), bXY = 0.5 (regression of X on Y).

Then: r = √(0.8 × 0.5) = √0.4 ≈ 0.632
Regression tells you: for every 1 unit increase in X, Y increases by 0.8 units
Correlation tells you: there is a moderately strong positive relationship (r = 0.63)
They describe the same dataset but answer completely different questions.

When to Use Which?

SituationUse
You want to know if study hours affect marksCorrelation
You want to predict marks for 6 hours of studyRegression
You want to know the direction of a relationshipCorrelation
You want to know the rate of changeRegression
You have no clear dependent/independent variableCorrelation
One variable clearly depends on anotherRegression
📌 One-Line Summary to Remember

Correlation measures; Regression predicts. They use related formulas and share the same numerator, but correlation gives you one number, while regression gives you an equation — and there's always a neat mathematical bridge between them: r = √(bYX × bXY)

Core Formulas

Regression Equations & Coefficients

For two variables X and Y, there are two regression lines.

(a) Regression Line of Y on X

Used to predict Y when X is given.

Y − Ȳ = bYX(X − X̄)

Or equivalently: Y = a + bX

(b) Regression Line of X on Y

Used to predict X when Y is given.

X − X̄ = bXY(Y − Ȳ)

Both lines pass through (X̄, Ȳ) — the means of X and Y

Regression Coefficients

Regression Coefficient of Y on X (bYX)

bYX = nΣXY − ΣX·ΣYnΣX² − (ΣX)²

Using deviations: bYX = ΣxyΣx², where x=X−X̄, y=Y−Ȳ

Also: bYX = r · σᵥσₓ

Regression Coefficient of X on Y (bXY)

bXY = nΣXY − ΣX·ΣYnΣY² − (ΣY)²

Also: bXY = r · σₓσᵥ

Frequently Tested

6 Properties of Regression Equations

These are important — questions are frequently asked on these!

Property 1

Both regression lines pass through (X̄, Ȳ) — the means of X and Y.

Property 2

The coefficient of correlation r is the geometric mean of the two regression coefficients:

r = ±√(bYX × bXY)

The sign of r matches the common sign of bYX and bXY.

Property 3

If one regression coefficient is greater than 1, the other must be less than 1 (they cannot both exceed 1 in absolute value, unless r = ±1).

Property 4

Both regression coefficients have the same sign — both positive or both negative.

Property 5

The regression coefficients are not symmetric: bYX ≠ bXY in general.

Property 6

−1 ≤ r ≤ 1, so bYX × bXY ≤ 1 always. This is your quickest check for validity.

🎯 Exam Tips

  • Always check the sign of regression coefficients — they must be the same sign
  • Use the Y on X line to predict Y, and the X on Y line to predict X
  • Verify your answer using Property 2: r² = bYX × bXY must be ≤ 1
Test Yourself

Practice MCQs — Regression Analysis

10 MCQs + 4 Assertion-Reason questions. Click Show Answer for the full explanation.

Q1 Concept
Who introduced the concept of regression, and what real-world observation led to it?
(a) Karl Pearson — correlation between height and weight
(b) Francis Galton — tall fathers having sons closer to average height
(c) Spearman — ranking of students
(d) Charles Darwin — natural selection
Answer: (b)
Sir Francis Galton introduced regression after observing that tall fathers' sons tended to be shorter than their fathers — heights "regressed" toward the population average.
Q2 Coefficients
A data analyst has already worked out both regression coefficients for her dataset: bYX = 0.6 and bXY = 0.4. What value of r should she report?
(a) 0.24
(b) 0.49
(c) 0.5
(d) 1.0
Answer: (b) 0.49
r = √(bYX×bXY) = √(0.6×0.4) = √0.24 ≈ 0.49.
Q3 Properties
Both lines of regression always pass through:
(a) The origin (0,0)
(b) The point (X̄, Ȳ)
(c) The point (1,1)
(d) They never intersect
Answer: (b)
Both regression lines pass through the means of X and Y — Property 1.
Q4 Validity
A student submits an assignment claiming her regression coefficients are bYX = 2.5 and bXY = 0.8. Before grading, you want to check: could these actually be valid regression coefficients?
(a) Yes, both are valid
(b) No, since bYX × bXY > 1, giving r > 1
(c) Yes, if r = 0
(d) Cannot be determined
Answer: (b)
2.5×0.8 = 2.0. Since r² = bYX×bXY must be ≤ 1, this is impossible — invalid (Property 6).
Q5 Sign
If bYX = −0.7, what must be true about bXY?
(a) bXY must be positive
(b) bXY must also be negative
(c) bXY can be any sign
(d) bXY must equal 0
Answer: (b)
Both regression coefficients always have the same sign (Property 4). Since bYX is negative, bXY must also be negative.
Q6 Prediction
An analyst has fitted the regression line of Y on X as Y = 3X + 20. If she now wants to predict Y for a new case where X = 10, what value should she get?
(a) 23
(b) 30
(c) 50
(d) 60
Answer: (c) 50
Y = 3(10)+20 = 30+20 = 50.
Q7 Independent/Dependent
In a study relating advertisement expenditure to sales, the independent variable is:
(a) Sales (since it's the outcome)
(b) Advertisement expenditure (since it's controlled/known)
(c) Both are independent
(d) Neither is independent
Answer: (b)
Advertisement expenditure is the predictor/explanatory variable (X). Sales is the response/dependent variable (Y) we want to predict.
Q8 Comparing r and b
Which statement correctly distinguishes correlation from regression?
(a) Both give an equation for prediction
(b) Correlation gives one number; regression gives an equation for prediction
(c) Regression is symmetric; correlation is not
(d) There is no real difference
Answer: (b)
Correlation (r) measures strength/direction only — one number. Regression gives an equation Y=a+bX that allows actual numeric prediction.
Q9 Using SD & r
If r = 0.6, σₓ = 5, σᵥ = 8, the value of bYX is:
(a) 0.375
(b) 0.6
(c) 0.96
(d) 1.5
Answer: (c) 0.96
bYX = r×σᵥσₓ = 0.6×85 = 0.6×1.6 = 0.96.
Q10 Conceptual
Why are there two lines of regression instead of just one?
(a) Because regression always has two unknowns
(b) Because predicting Y from X and predicting X from Y are different problems, so each needs its own line
(c) Because correlation requires two lines
(d) There is actually only one line in regression
Answer: (b)
Regression is not symmetric (Property 5). The "best line" for predicting Y given X minimizes a different error than the "best line" for predicting X given Y — hence two distinct lines.
Assertion-Reason Questions (AR 1–4)
AR 1 Regression Lines
Assertion (A): The two lines of regression (Y on X, and X on Y) are generally different lines.

Reason (R): Regression coefficients bYX and bXY are usually not equal, except when r = ±1.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R does NOT explain A
(c) A is true, R is false
(d) A is false, R is true
Answer: (a)
Regression is not symmetric: bYX ≠ bXY generally. When r=±1, the two lines coincide. R correctly explains why A is true.
AR 2 Coefficients
Assertion (A): If bYX = 0.6 and bXY = 0.4, the correlation coefficient r ≈ 0.49.

Reason (R): The correlation coefficient is the geometric mean of the two regression coefficients: r = ±√(bYX × bXY).
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R does NOT explain A
(c) A is true, R is false
(d) A is false, R is true
Answer: (a)
r = √(0.6×0.4) = √0.24 ≈ 0.49 ✓. R states the exact formula used and directly explains A.
AR 3 Validity
Assertion (A): bYX = −0.7 and bXY = 0.8 cannot be the regression coefficients of the same data set.

Reason (R): Both regression coefficients must always carry the same sign.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R does NOT explain A
(c) A is true, R is false
(d) A is false, R is true
Answer: (a)
One coefficient is negative, the other positive — violates Property 4 (same sign required), so A is true. R states this exact property and directly explains A.
AR 4 Correlation vs Regression
Assertion (A): A strong correlation between two variables proves that one causes the other.

Reason (R): Correlation only measures the strength and direction of a linear association, not a cause-and-effect relationship.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R does NOT explain A
(c) A is true, R is false
(d) A is false, R is true
Answer: (d)
A is false: correlation does NOT prove causation — two variables can be correlated due to a third factor or coincidence. R is true and correctly states the limitation, which is precisely why A is false.
Quick Concept Checks

Short Answer Questions

9 quick, 1-3 mark style questions. Click Show Solution to reveal complete working.

Q1 Finding r from Regression Coefficients
Given bYX = 0.8 and bXY = 0.2. Find the coefficient of correlation.
r = ±√(bYX × bXY) = ±√(0.8 × 0.2) = ±√0.16 = ±0.4
Since both regression coefficients are positive, r is also positive
✓ r = +0.4
Q2 Checking Validity of Regression Coefficients
Can bYX = 2.5 and bXY = 0.8 be the regression coefficients of a dataset?
Check: bYX × bXY = 2.5 × 0.8 = 2.0
Since r² = bYX×bXY = 2.0 > 1, this would give r > 1, which is impossible
✗ These CANNOT be valid regression coefficients
Quick Concept Checks
Q3 Naming the Lines
Name the two lines of regression for variables X and Y.
Regression has exactly two lines, because predicting Y from X and predicting X from Y are different problems
✓ Line of Y on X: Y−Ȳ = bYX(X−X̄)  |  Line of X on Y: X−X̄ = bXY(Y−Ȳ)
Q4 r from Coefficients
If bYX = 0.6 and bXY = 0.4, find r.
r = ±√(bYX × bXY) = ±√(0.6 × 0.4) = ±√0.24
Both coefficients positive → r is positive
✓ r ≈ 0.49
Q5 Common Point
Both lines of regression pass through which point?
Property 1 states both lines always intersect at the means of the two variables
✓ (X̄, Ȳ) — the point representing the mean of X and the mean of Y
Q6 Validity Check
State whether the following can be regression coefficients: bYX = −0.7, bXY = 0.8. Give reason.
Property 4: both regression coefficients must always have the same sign
Here bYX is negative and bXY is positive — opposite signs
✗ Not valid — bYX and bXY must share the same sign, which they don't here
Q7 Using r and SD
If r = 0.9, σₓ = 4, σᵥ = 5, find bYX.
bYX = r·(σᵥ/σₓ) = 0.9×(5/4) = 0.9×1.25
✓ bYX = 1.125
Building Equations & Comparing Concepts
Q8 Finding bYX from Raw Data
A researcher records the number of hours of sunlight (X) and the height of a sapling in cm (Y) over 5 weeks. Find the regression coefficient bYX from the following data:
X13579
Y468911
n=5, ΣX=25, ΣY=38, ΣXY=224, ΣX²=165
bYX = [5(224)−25×38] / [5(165)−25²] = (1120−950)/(825−625) = 170/200
✓ bYX = 0.85
Q9 Given the Line, Find Ȳ
If the line of regression of Y on X is Y = 2X + 3 and X̄ = 5, find Ȳ.
The regression line always passes through (X̄, Ȳ)
Substitute X=5: Y = 2(5)+3
✓ Ȳ = 13

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Full Derivations

Long Answer Questions

8 multi-step, 4-5 mark style questions with complete solutions.

Q1 Building Equations from a Table
Marks in Mathematics (X) and Science (Y) for 5 students:
X246810
Y579811
Find: (i) both regression equations, (ii) estimate Y when X = 7.
Step 1 — Build the table:
XYX²Y²XY
2542510
47164928
69368154
88646464
1011100121110
ΣX=30ΣY=40ΣX²=220ΣY²=340ΣXY=266
n = 5. Step 2 — Means: X̄ = 30/5 = 6, Ȳ = 40/5 = 8
Step 3 — Find bYX: bYX = 5(266) − 30×405(220) − 30² = 1330 − 12001100 − 900 = 130200 = 0.65
Step 4 — Find bXY: bXY = 1330 − 12005(340) − 40² = 1301700 − 1600 = 130100 = 1.3
Step 5 — Line of Y on X: Y−8 = 0.65(X−6) → Y = 0.65X + 4.1
Step 6 — Line of X on Y: X−6 = 1.3(Y−8) → X = 1.3Y − 4.4
Step 7 — Estimate Y when X=7: Y = 0.65(7)+4.1 = 4.55+4.1 = 8.65
✓ Y = 0.65X + 4.1  |  X = 1.3Y − 4.4  |  Y at X=7 is 8.65
Q2 Using Means, SD and r
For two variables X and Y: X̄=40, Ȳ=45, σₓ=6, σᵥ=8, r=0.75. Find both regression equations.
bYX = r·σᵥσₓ = 0.75×86 = 0.75×1.333 = 1.0
bXY = r·σₓσᵥ = 0.75×68 = 0.75×0.75 = 0.5625
Line of Y on X: Y−45 = 1.0(X−40) → Y = X + 5
Line of X on Y: X−40 = 0.5625(Y−45) → X = 0.5625Y + 14.69
✓ Y = X + 5  |  X = 0.5625Y + 14.69
Q3 Two Equations Given
The two regression equations of X and Y are: 5X − Y = 22 and 64X − 45Y = 24. Find X̄, Ȳ, and r.
Both lines pass through (X̄, Ȳ), so solve the two equations simultaneously
From 5X−Y=22: Y=5X−22. Substituting into 64X−45Y=24: 64X−45(5X−22)=24 → −161X=−966 → X̄=6
Ȳ = 5(6)−22 = 8
To find bYX and bXY, test which equation is "Y on X" vs "X on Y": treating 64X−45Y=24 as Y on X gives bYX=64/45≈1.422; treating 5X−Y=22 as X on Y gives bXY=1/5=0.2 (this is the only assignment where bYX×bXY ≤ 1)
r = √(1.422 × 0.2) = √0.284
✓ X̄ = 6, Ȳ = 8, r ≈ 0.53
Q4 Given Coefficients & Means
Given X̄=25, Ȳ=30, bYX=1.2, bXY=0.4. Find the two lines of regression. Also find Y when X=28.
Line of Y on X: Y−30 = 1.2(X−25) → Y = 1.2X − 30 + 30 = 1.2X
Line of X on Y: X−25 = 0.4(Y−30) → X = 0.4Y + 13
At X=28: Y = 1.2(28) = 33.6
✓ Y on X: Y=1.2X  |  X on Y: X=0.4Y+13  |  Y at X=28 is 33.6
Q5 Conceptual — Distinguish
Distinguish between correlation and regression with two examples from daily life.
Correlation measures strength/direction only — one number (r), no prediction. Regression gives an equation that predicts one variable from another.
Example 1 (Correlation): "Are ice-cream sales and temperature related?" → r tells you how strongly, not how much sales change per degree.
Example 2 (Regression): "Predict next month's sales if temperature is 35°C" → needs a regression equation, not just r.
✓ Correlation answers "how strongly related?"; Regression answers "what is the predicted value?"
Q6 Complete Regression from Raw Data
A small business tracks the number of website visits (X) it gets each day against the number of orders placed (Y) on those same days, recorded over 5 days. Calculate the two regression equations from the following data, and estimate the expected orders when website visits reach 12.
X58101215
Y1014161822
n=5, ΣX=50, ΣY=80, ΣXY=868, ΣX²=558, ΣY²=1360. X̄=10, Ȳ=16
bYX = [5(868)−50×80]/[5(558)−50²] = (4340−4000)/(2790−2500) = 340/290 ≈ 1.172
bXY = (4340−4000)/[5(1360)−80²] = 340/400 = 0.85
Line of Y on X: Y−16 = 1.172(X−10) → Y = 1.172X + 4.28
At X=12: Y = 1.172(12)+4.28 = 14.06+4.28
✓ Y on X: Y=1.172X+4.28  |  Estimated Y at X=12 ≈ 18.35
Q7 Given Summary Statistics
A quality control engineer has already calculated the summary statistics for two related production measurements: n=10, ΣX=60, ΣY=80, ΣX²=450, ΣY²=720, and ΣXY=540. Using only these summary values, find: (i) the line of Y on X, (ii) the line of X on Y, and (iii) the correlation coefficient r.
X̄=6, Ȳ=8
bYX = [10(540)−60×80]/[10(450)−60²] = (5400−4800)/(4500−3600) = 600/900 ≈ 0.667
bXY = (5400−4800)/[10(720)−80²] = 600/800 = 0.75
(i) Y on X: Y−8 = 0.667(X−6) → Y = 0.667X + 4
(ii) X on Y: X−6 = 0.75(Y−8) → X = 0.75Y
(iii) r = √(0.667 × 0.75) = √0.5
✓ (i) Y=0.667X+4  |  (ii) X=0.75Y  |  (iii) r ≈ 0.707
Q8 Both Lines from r and SD
For two variables: r=0.6, σₓ=1.5, σᵥ=2, X̄=10, Ȳ=20. (i) Find both regression equations. (ii) Find X when Y=25. (iii) Find Y when X=12.
bYX = r·(σᵥ/σₓ) = 0.6×(2/1.5) = 0.8
bXY = r·(σₓ/σᵥ) = 0.6×(1.5/2) = 0.45
(i) Y on X: Y−20 = 0.8(X−10)  ·  X on Y: X−10 = 0.45(Y−20)
(ii) At Y=25: X = 10+0.45(25−20) = 10+2.25
(iii) At X=12: Y = 20+0.8(12−10) = 20+1.6
✓ (i) Both equations above  |  (ii) X = 12.25  |  (iii) Y = 21.6

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Real-World Applications

Case Studies

3 application-based questions showing regression used in real decisions.

Q1 Predicting from a Regression Line (Real-World)
A company's advertising spend (X, ₹ lakh) and sales (Y, ₹ lakh) have regression equation of Y on X: Y = 3X + 20. (i) Predict sales when spend is ₹15 lakh. (ii) If X̄=10, find Ȳ.
(i) When X=15: Y = 3(15)+20 = 45+20 = ₹65 lakh
(ii) Since the line passes through (X̄, Ȳ): Ȳ = 3(10)+20 = ₹50 lakh
✓ (i) ₹65 lakh predicted sales  |  (ii) Ȳ = ₹50 lakh
Q2 Real-World — Age & Blood Pressure
Age (X) and blood pressure (Y) of 8 patients:
Age (X)5263453672654725
BP (Y)6253512579436033
Find the regression equation of Y on X. Predict BP for age 50.
n=8, ΣX=405, ΣY=406, ΣXY=21886, ΣX²=22237. X̄=50.625, Ȳ=50.75
bYX = [8(21886)−405×406]/[8(22237)−405²] = (175088−164430)/(177896−164025) = 10658/13871 ≈ 0.768
Line of Y on X: Y−50.75 = 0.768(X−50.625) → Y = 0.768X + 11.85
At X=50: Y = 0.768(50)+11.85 = 38.4+11.85
✓ Y on X: Y = 0.768X + 11.85  |  Predicted BP at age 50 ≈ 50.27
Q3 Application — School Predicting Final Score
A school predicts final exam score (Y) from mid-term score (X). Data from 6 students:
Mid-term (X)405060708090
Final (Y)455560708092
(a) Find the regression line of Y on X. (b) Predict the score of a student who scored 75 in mid-term. (c) Calculate r and comment on the strength.
n=6, ΣX=390, ΣY=402, ΣXY=27730, ΣX²=27100, ΣY²=28414. X̄=65, Ȳ=67
bYX = [6(27730)−390×402]/[6(27100)−390²] = (166380−156780)/(162600−152100) = 9600/10500 ≈ 0.914
bXY = (166380−156780)/[6(28414)−402²] = 9600/8880 ≈ 1.081
(a) Y on X: Y−67 = 0.914(X−65) → Y = 0.914X + 7.57
(b) At X=75: Y = 0.914(75)+7.57 = 68.55+7.57
(c) r = √(0.914 × 1.081) = √0.988
✓ (a) Y = 0.914X + 7.57  |  (b) Predicted score ≈ 76.1  |  (c) r ≈ 0.994 — extremely strong positive correlation between mid-term and final scores

📌 Quick Formula Card

FormulaDescription
bYX = nΣXY − ΣX·ΣYnΣX² − (ΣX)²Regression coeff. Y on X
bXY = nΣXY − ΣX·ΣYnΣY² − (ΣY)²Regression coeff. X on Y
r = ±√(bYX·bXY)Correlation from regression
bYX = r·σᵥσₓUsing SD and r
bXY = r·σₓσᵥUsing SD and r
Avoid Losing Marks

Common Mistakes in Regression Questions

These specific errors show up again and again in student answers.

❌ Watch Out For These

  • Using the line of X on Y when the question asks to predict Y from a given X (always match the line to the prediction direction)
  • Assuming bYX = bXY — they are almost always different numbers
  • Forgetting that both regression coefficients must carry the same sign
  • Treating a strong r value as proof of cause and effect — it only shows association
  • Skipping the step of writing Y−Ȳ = bYX(X−X̄) before simplifying — this earns the formula mark
  • Not verifying bYX × bXY ≤ 1 when asked to check if given coefficients are valid
  • Confusing "regression of Y on X" with "regression of X on Y" when substituting which variable is X̄ vs Ȳ
Common Questions

Frequently Asked Questions

Questions students ask most about Regression Analysis.

No, they are not the same, though they are closely related. Correlation measures the strength and direction of a relationship using a single value r between −1 and +1. Regression gives an equation that lets you predict one variable's value from another. Correlation tells you if two variables move together; regression tells you exactly how much one changes for a given change in the other.
The regression coefficient of Y on X is bYX = nΣXY − ΣX·ΣYnΣX² − (ΣX)². It can also be written as bYX = r × σᵥσₓ, using the correlation coefficient and standard deviations.
There are two lines because regression is not symmetric. The line of Y on X is used to predict Y when X is known, and the line of X on Y is used to predict X when Y is known. These two lines are generally different unless the correlation coefficient r equals ±1.
The correlation coefficient r is the geometric mean of the two regression coefficients bYX and bXY: r = ±√(bYX × bXY). This means bYX × bXY can never exceed 1 — a handy validity check for any pair of regression coefficients.
Yes. Both the line of Y on X and the line of X on Y always pass through the point representing the means of X and Y, written as (X̄, Ȳ). This is one of the six key properties of regression equations covered on this page.
Yes — Regression Analysis is officially syllabus topic 6.4 under Unit 5: Descriptive Statistics in the CBSE 2026-27 Applied Mathematics curriculum for Class 11. It covers the concept of regression, dependent and independent variables, regression coefficients, regression equations, and their properties. Since it's a recently added topic with limited textbook coverage, this page exists to give you everything in one place.
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Unit 5
Back to Descriptive Statistics — MCQs, Examples & Case Studies
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Financial Mathematics
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