Chapter 4, Problem 20PT

(a)

To determine

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

Answer to Problem 20PT

The equation of the regression line is $Y=0.325X+0.89$ .

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 = 25632

Mean X = 2

Mean Y = 5126.4

Sum of squares (SSX) = 10

Sum of products (SP) = 6264

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

Here,

  $\begin{array}{l}b=\frac{SP}{SSX}=\frac{6264}{10}=\text{ 626}\text{.4}\\ a=\left(Meany\right)-b\left(MeanX\right)=\text{ 5126}\text{.4 }-\left(626.4\times 2\right)=\text{ 3873}\text{.6}\end{array}$

Substitute the values of a andb .

The equation of the regression line is $Y=626.4X+3873.6$

The plot for the regression line is:

  

(b)

To determine

To predict:The number of children in Russia who will be adopted in the year 2025.

Answer to Problem 20PT

In year 2025, $19533.6$ children will be adopted.

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 = 25632

Mean X = 2

Mean Y = 5126.4

Sum of squares (SSX) = 10

Sum of products (SP) = 6264

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

Here,

  $\begin{array}{l}b=\frac{SP}{SSX}=\frac{6264}{10}=\text{ 626}\text{.4}\\ a=\left(Meany\right)-b\left(MeanX\right)=\text{ 5126}\text{.4 }-\left(626.4\times 2\right)=\text{ 3873}\text{.6}\end{array}$

Substitute the values of a andb .

The equation of the regression line is $Y=626.4X+3873.6$

In the equation above, substitute 25 for X .

  $\begin{array}{c}Y=626.4\times 25+3873.6\\ =19533.6\end{array}$

Therefore, a total of $19533.6$ children will be adopted in the year 2025.