M L Aggarwal Solutions for Chapter: Linear Regression, Exercise 2: CHAPTER TEST

Two random variables have Regression lines $3x+2y-26=0 \mathrm{and} 6x+y-31=0.$ Calculate the standard deviation of $y$, given variance of $x$ is $25.$

The following table shows the ages $x$ and systolic blood pressure $y$ of $12$ women.

Find the correlation coefficient between $x$ and $y$. (Answer upto two places of decimal)

The following table shows the ages $x$ and systolic blood pressure $y$ of $12$ women.

Estimate the blood pressure of a woman whose age is $45$ years.

The following table show final grades of $10$ students in Algebra and Physics.

The following table show final grades of $10$ students in Algebra and Physics.

If $x$ and $y$ are a pair of correlated variables. Ten observations of their values $(x_i,y_i)$ have the following results :

$\sum _{}^{}{x}_i=55, \sum _{}^{}{y}_i=55, \sum _{}^{}{x}_i{y}_i=350 and \sum _{}^{}{x_i}^2=385.$

Predict the value of $y$ when the value of $x$ is $6.$

The coefficient of correlation between the ages of husbands and wives in a community was found to be $0.8,$ the mean of husband's age was $25$ years and that of wives $22$ years. Their standard deviations were $4$ and $5$ years respectively. Find the expected age of husband when wife's age is $22$ years.

The coefficient of correlation between the ages of husbands and wives in a community was found to be $0.8,$ the mean of husband's age was $25$ years and that of wives $22$ years. Their standard deviations were $4$ and $5$ years respectively. Find the expected age of wife when husband's age is $33$ years.