Skip to content
← Business Mathematics and Statistics

Business Mathematics and Statistics · Class 11 Commerce

Ch 9Correlation and Regression Analysis — Class 11 Business Mathematics and Statistics, concept-first.

Every statistical idea studied so far — mean, dispersion, probability — has described a single variable at a time. Many real business questions instead ask about the relationship between two variables measured on the same set of items: does higher advertising spend go with higher sales, does more experience go with a h…

31

Q&A

5

Concepts

Not available

Exam weightage

Start learning — read this chapter →

Key concepts

Hover a concept to preview it and jump to its most relevant Q&A.

Karl Pearson's Coefficient of Correlation

Pearson's (or the equivalent direct-method formula) is a unit-free number between and measuring the strength and direction of the linear relationship between two variables, independent of the units either is measured in.

Most relevant Q&A

Start with this concept →

Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

1

Bivariate Data and the Scatter Diagram

Every statistical idea studied so far — mean, dispersion, probability — has described a single variable at a time.

2

Karl Pearson's Coefficient of Correlation

Karl Pearson's coefficient of correlation, usually written , puts an exact, unit-free number on the strength and direction of a linear relationship between two variables.

3

Spearman's Rank Correlation Coefficient

Pearson's needs actual numerical values to work with. Sometimes the available data is only an order — two judges ranking the same set of contestants, two examiners ranking the same essays — with no un…

4

Regression Coefficients — byx and bxy

Correlation tells us how strongly two variables are linearly related, but not how to predict one from the other.

5

Regression Lines and Their Point of Intersection

Each regression coefficient of the previous section is the slope of a regression line, used for prediction.

Exercises

+Show 6 questions6 questions
  1. Q6The number of hours studied ($x$) and marks obtained out of 50 ($y$) by 5 students are given below. Find Karl Pearson's coefficient of corre…Free
  2. Q7Two judges, A and B, scored 5 contestants in a competition out of 50 marks each, as shown below. Convert each judge's scores to ranks (rank…Free
  3. Q8For a bivariate data set, $\text{Cov}(x,y)=18$, $\text{Var}(x)=36$, and $\text{Var}(y)=16$. Find (i) Karl Pearson's coefficient of correlati…Preview
  4. Q9The regression line of $y$ on $x$ for a set of bivariate data is $3x-2y=1$, and the regression line of $x$ on $y$ is $4x-y=5$. Find the mean…Preview
  5. Q10The following table shows the years of experience ($x$) and monthly salary in ₹'000 ($y$) of 5 employees. Find (i) Karl Pearson's correlatio…Preview
  6. Q11For the following data on a company's monthly advertising expenditure ($x$, ₹'000) and units sold ($y$), state — from the shape a scatter di…Preview

Sample & Board Papers

Sample papers and previous-year board questions for this subject.

+Show 20 questions20 questions
  1. Q1If two variables move in decreasing direction then the correlation is : (a) negative (b) positive (c) perfect negative (d) no correlationPreview
  2. Q2Which statement is correct ? (a) X and Y are two variables, there can be at the most more regression. (b) Co-efficient of correlation lies b…Preview
  3. Q3Find the Regression lines X on Y from the following data : $N = 25$, $\sum X = 125$, $\sum Y = 100$, $\sum X^2 = 650$, $\sum Y^2 = 436$, $\s…Preview
  4. Q4Calculate the correlation co-efficient from the following data : $N = 9$, $\sum X = 45$, $\sum Y = 108$, $\sum X^2 = 285$, $\sum Y^2 = 1356$…Preview
  5. Q5If the values of two variables move in opposite direction then the correlation is said to be : (a) Perfect positive (b) Negative (c) No corr…Preview
  6. Q6Example for positive correlation is : (a) Repayment period and EMI (b) Income and expenditure (c) Weight and Income (d) Price and demandPreview
  7. Q7Calculate the co-efficient of correlation from the following data : $\Sigma X = 50$, $\Sigma Y = -30$, $\Sigma X^{2} = 290$, $\Sigma Y^{2} =…Preview
  8. Q8The rank of 10 students of same batch in two subjects A and B are given below. Calculate the rank correlation coefficient. | Rank of A | 1 |…Preview
  9. Q9If X and Y are two variables then there can be atmost : (a) Three regression lines (b) One regression line (c) More regression lines (d) Two…Preview
  10. Q10If the value of the two variables move in same direction, then the correlation is said to be : (a) Perfect positive (b) Negative (c) No corr…Preview
  11. Q11Calculate the correlation co-efficient from the following data. $N = 9$, $\Sigma X = 45$, $\Sigma Y = 108$, $\Sigma X^2 = 285$, $\Sigma Y^2…Preview
  12. Q12The following are ranks obtained by 10 students in Commerce and Accountancy. | Commerce | 6 | 4 | 3 | 1 | 2 | 7 | 9 | 8 | 10 | 5 | | --- | -…Preview
  13. Q13(a) Calculate the coefficient of correlation for the ages of husbands and their respective wives. | Age of husbands | 23 | 27 | 28 | 29 | 30…Preview
  14. Q14The correlation coefficient : (a) $r=b_{xy}\times b_{yx}$ (b) $r=\pm\sqrt{b_{xy}\times b_{yx}}$ (c) $r=\pm\sqrt{\dfrac{1}{b_{xy}\times b_{yx…Preview
  15. Q15Correlation co-efficient lies between : (a) $-1$ to $0$ (b) $0$ to $\infty$ (c) $-1$ to $\infty$ (d) $-1$ to $+1$Preview
  16. Q16(a) The following are the ranks obtained by 10 students in Commerce and Accountancy are given below : | Commerce | 6 | 4 | 3 | 1 | 2 | 7 | 9…Preview
  17. Q17When one regression coefficient is negative, the other would be : (a) Positive (b) Zero (c) Negative (d) None of themPreview
  18. Q18The term regression was introduced by : (a) Karl Pearson (b) R.A. Fisher (c) Croxton and Cowden (d) Sir Francis GaltonPreview
  19. Q19Calculate the correlation coefficient from the following data. $N=9$, $\Sigma X=45$, $\Sigma Y=108$, $\Sigma X^2=285$, $\Sigma Y^2=1356$, $\…Preview
  20. Q20The rank of 10 students of same batch in two subjects A and B are given below. Calculate the rank correlation coefficient. | Rank of A | 1 |…Preview

More questions

+Show 5 questions5 questions
  1. Example 1The monthly advertising expenditure ($x$, in ₹'000) and the corresponding sales ($y$, in ₹ lakh) of a company over 5 months are given below.…Free
  2. Example 2The price ($x$, in ₹) of a commodity and the quantity demanded ($y$, in units) over 5 weeks are given below. Find Karl Pearson's coefficient…Free
  3. Example 3The ranks given by two examiners, A and B, to 6 candidates in an interview are shown below. Find Spearman's rank correlation coefficient bet…Preview
  4. Example 4Using the same advertising and sales data as Worked Example 1 ($\bar x=3,\bar y=4$, $\sum(x-\bar x)(y-\bar y)=6$, $\sum(x-\bar x)^2=10$, $\s…Preview
  5. Example 5Using $\bar x=3$, $\bar y=4$, $b_{yx}=0.6$ and $b_{xy}=1.0$ from Worked Example 4, write down the two regression line equations and verify t…Preview