Question

The average number of people in a family that attended college for various years is given in Table 12.29.

a. Using “year” as the independent variable and “Number of Family Members Attending College” as the dependent variable, draw a scatter plot of the data.

b. Calculate the least-squares line. Put the equation in the form of: \(\hat{y}=a+bx\)

c. Find the correlation coefficient. Is it significant?

Short answer

Part a.

Part b. \(\hat{y}=88.7206-0.0432\)

Part c. \(r=-0.8533\);yes

Step-by-step solution

Part a. Step 1. Explanation

Just plot the “year” as x variable and “Number of Family Members Attending College” as y variable.

Number of family Members Attending College

Part b. Step 1. Explanation

\(\hat{y}=a+bx\)

Here \(b\) is the slope and \(a\) is the interception

X	1969	1973	1975	1979	1983	1988	1991
Y	4.0	3.6	3.2	3.0	3.0	3.0	2.9

\(b=\frac{n(\sum XY)-(\sum X)(\sum Y)}{n(\sum X^{2})-(\sum X)^{2}}\)

\(b=\frac{7(44922.7)-(13858)(22.7)}{7(27435270)-(13858)^{2}}\)

\(b=-0.043176\)

\(a=\frac{(\sum Y)-b(\sum X)}{n}\)

\(a=\frac{(22.7)-(-0.043176)(13858)}{7}\)

\(a=88.719\)

Therefore, least square line is \(\hat{y}=88.7206-0.0432x\)