Chapter 1.1, Problem 46E

(a)

To determine

To find:The linear regression equation for the given data.

Answer to Problem 46E

The linear regression equation for the given data is $y=0.680027x+9.012539$ .

Explanation of Solution

Given information:The table given below shows the ages and weights of nine girls:

Girl’s ages and weights
Age (months)	Weight (pounds)
19	22
21	23
24	25
27	28
29	31
31	28
34	32
38	34
43	39

Calculation:

To find the linear regression equation of the given data, use graphing calculator.

Step 1: Press $\boxed{\text{STAT}}\boxed{1}$ keys to enter the given data.

Step 2: List the input values 19, 21, 24, 27, 29, 31, 34, 38 and 43 in the L1 column.

Step 3: List the input values 22, 23, 25, 28, 31, 28, 32, 34 and 39 in the L2 column.

Step 4: Press the keystrokes $\boxed{\text{STAT}}\boxed{\Rightarrow }\boxed{4}\boxed{\text{ENTER}}$ to find line of regression and again press $\boxed{\text{ENTER}}$ key. So, the linear regression equation for the given data is:

  $y=0.680027x+9.012539$

Therefore, thelinear regression equation for the given data is $y=0.680027x+9.012539$ .

(b)

To determine

To find: The slope of the regression line for the given data and describe the representation of the slope.

Answer to Problem 46E

The slope of the regression line for the given data is 0.68 and it represents the average weight in pounds per month gain in girls from 1 to 4 years old.

Explanation of Solution

Given information:The table given below shows the ages and weights of nine girls:

Girl’s ages and weights
Age (months)	Weight (pounds)
19	22
21	23
24	25
27	28
29	31
31	28
34	32
38	34
43	39

Calculation:

From part (a), the linear regression equation for the given data is $y=0.680027x+9.012539$ .

It is known that slope-form of a line is $y=mx+c$ . Compare the above equation with this equation.

  $m\approx 0.68$

Therefore, the slope of the regression line for the given data is 0.68 and it represents the average weight in pounds per month gain in girls from 1 to 4 years old.

(c)

To determine

To plot: The graph of the linear regression equation on a scatter plot for the given data.

Explanation of Solution

Given information:The table given below shows the ages and weights of nine girls:

Girl’s ages and weights
Age (months)	Weight (pounds)
19	22
21	23
24	25
27	28
29	31
31	28
34	32
38	34
43	39

Graph:

To make the scatter plot enter the data, then follow the stepsusing graphing calculator.

Step 1: Press $\boxed{2\text{nd}}\boxed{\text{Y}=}$ and make sure that Plot 1 is ON. Choose the scatter plot icon in type.

Step 2: Press $\boxed{\text{GRAPH}}$ key. Set the window at $\left[15,45\right]$ with scale 5 by $\left[20,40\right]$ with scale 2.

Step 3: Press the keystrokes $\boxed{\text{STAT}}\boxed{\Rightarrow }\boxed{4}\boxed{2\text{nd}}\boxed{1}\boxed{,}\boxed{2\text{nd}}\boxed{2}\boxed{,}\boxed{\text{VARS}}\boxed{\Rightarrow }\boxed{1}\boxed{1}\boxed{\text{ENTER}}$ . Now, press $\boxed{\text{GRAPH}}$ and $\boxed{\text{TRACE}}$ key to plot the graph as shown below.

  

Figure (1)

Interpretation:From the graph it can be interpreted that the weight of girls is increasing as there is increasing.

(d)

To determine

To find: The weight of 30 month old girl by using the regression equation.

Answer to Problem 46E

The approximate weight of 30 month old girl is 29.4 pounds.

Explanation of Solution

Given information:The table given below shows the ages and weights of nine girls:

Girl’s ages and weights
Age (months)	Weight (pounds)
19	22
21	23
24	25
27	28
29	31
31	28
34	32
38	34
43	39

Calculation:

From part (a), the linear regression equation for the given data is $y=0.680027x+9.012539$ .

To find the weight of 30 month old girl, substitute 30 for $x$ in the above equation.

  $\begin{array}{c}y=0.680027\left(30\right)+9.012539\\ =20.40081+9.012539\\ \approx 29.4\end{array}$

Therefore, the approximate weight of 30 month old girl is 29.4 pounds.