Chapter 4, Problem 10STP

(a)

To determine

To write:The slope intercept form of the equation of regression line for the data given in table.

Answer to Problem 10STP

The equation of the regression line is $Y=0.45X$ .

Explanation of Solution

Given:

The table is:

  

Calculation:

The equation for the regression line can be calculated by performing the following calculations.

Sum of X = 10

Sum of Y = 4.5

Mean X = 2.5

Mean Y = 1.125

Sum of squares (SSX) = 5

Sum of products (SP) = 2.25

Regression Equation = $\text{Y }=bX+a$

Here,

  $\begin{array}{l}b=\frac{SP}{SSX}=\frac{2.25}{5}=\text{ 0}\text{.45}\\ a=\left(Meany\right)-b\left(MeanX\right)=\text{ 1}\text{.13 }-\left(0.45\times 2.5\right)=\text{ 0}\end{array}$

Substitute the values of a and b .

The equation of the regression line is $Y=0.45X$

The plot for the regression line is:

  

(b)

To determine

To describe:The relation between the hour and the amount of rain received.

Answer to Problem 10STP

The relation between the hour and amount of rain received is direct with a slope of 0.45.

Explanation of Solution

Given:

The table is:

  

The equation of the regression fit line comes out to be $Y=0.45X$ . This relation defines the amount of rain received with the hour. It can be observed that amount of rain in inches is directly proportional to the rain received for the number of hours.

The slope of the equation defines the direct relationship between the number of hours and the amount of rain received.