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Business Mathematics and Basic Statistics · Class 12 Commerce

Ch 16Bivariate Statistics — Correlation and Regression — Class 12 Business Mathematics and Basic Statistics, concept-first.

So far, every measure this course has looked at — mean, mode, median, dispersion — has described a single variable at a time: marks in one subject, wages of one factory's workers, ages of one clinic's patients.

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Q&A

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Concepts

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Unit weightage

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Key concepts

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Bivariate Data and Covariance

Bivariate data pairs two measurements for each unit of observation (e.g. advertising expenditure and sales for each month).

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Chapter contents

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

1

Idea of Bivariate Data and Covariance

So far, every measure this course has looked at — mean, mode, median, dispersion — has described a single variable at a time: marks in one subject, wages of one factory's workers, ages of one clinic's…

2

Pearson's Correlation Coefficient

Covariance tells us the direction in which two variables move together, but its size is tied to whatever units and happen to be measured in, so a covariance of, say, 1.2 carries no meaning on its own…

3

Spearman's Rank Correlation Coefficient

Pearson's correlation coefficient needs actual numerical values of and to work with. Sometimes, though, the data available is only an order — two judges ranking the same contestants, or two examiners…

4

Regression Coefficients — byx and bxy

Correlation tells us how strongly two variables are linearly related, but it does not by itself give a way to predict one variable's value from the other's.

5

Regression Lines and Their Point of Intersection

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

Exercises

+Show 6 questions6 questions
  1. Q7The number of hours studied ($x$) and marks obtained out of 50 ($y$) by 5 students are given below. Find the covariance between hours studie…Free
  2. Q8Find Pearson's correlation coefficient for the following data using the deviation method. | $x$ | 2 | 3 | 5 | 4 | 6 | |---|---|---|---|---|-…Free
  3. Q9Two 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…Preview
  4. Q10Using the same data as Exercise Question 2 ($x:2,3,5,4,6$; $y:3,4,2,5,6$), find the two regression coefficients $b_{yx}$ and $b_{xy}$, and v…Preview
  5. Q11The 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
  6. Q12The following table shows the advertising expenditure ($x$, in ₹'000) and sales ($y$, in ₹'0000) of a company over 5 quarters. Find (i) Pear…Preview

More questions

+Show 6 questions6 questions
  1. Example 1The monthly advertising expenditure ($x$, in ₹'000) and the corresponding sales ($y$, in ₹ lakh) of a small company over 5 months are given…Free
  2. Example 2Using the same advertising expenditure and sales data as Worked Example 1, find Pearson's correlation coefficient between the two variables.Free
  3. Example 3The price ($x$, in ₹) of a commodity and the quantity demanded ($y$, in units) over 5 weeks are given below. Find Pearson's correlation coef…Preview
  4. Example 4The 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
  5. Example 5Using the same advertising expenditure and sales data as Worked Examples 1 and 2 (covariance $=1.2$, $\text{Var}(x)=2$, $\text{Var}(y)=1.2$)…Preview
  6. Example 6Using $\bar{x}=3$, $\bar{y}=4$, $b_{yx}=0.6$ and $b_{xy}=1.0$ from Worked Examples 1, 2 and 5, write down the two regression line equations…Preview