Tamil Nadu Board Solutions for Chapter: Regression Analysis, Exercise 1: Exercise

Compute the two regression equations from the following data.

If $X=3.5$ what will be the value of $Y$?

Explain in detail the uses of regression analysis.

Distinguish between correlation and regression

Interpret the result for the given information. A simple regression line is fitted for a data set and its intercept and slope respectively are $2$ and $3$. Construct the linear regression of the form $Y=a+bx$ and offer your interpretation for $a$ and $b$. If $X$ is increased from $1$ to $2$, what is the increase in $Y$ value. Further if $X$ is increased from $2$ to $5$ what would be the increase in $Y$. Demonstrate your answer mathematically.

Using the method of least square, calculate the regression equation of $X$ on $Y$ and $Y$ on $X$ from the following data and estimate $X$ where $Y$ is $16$.

Also determine the value of correlation coefficient

The following table shows the age $\left(X\right)$ and systolic blood pressure $\left(Y\right)$ of $8$ persons.

Fit a simple linear regression model, $Y$ on $X$  and estimate the blood pressure of a person of $60$ years.

Find the regression equation of $X$ on $Y$ given that $n=5$, $\sum x = 30$, $\sum y = 40$, $\sum xy = 214$, $\sum x^2 = 220$,$\sum y^2 = 340$.

Find the linear regression equation of percentage worms $\left(Y\right)$ on size of the crop $\left(X\right)$ based on the following seven observations.