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Magazine Chapter 12: Q. 78 (page 730)
The average number of people in a family that attended college for various years is given in Table 12.29.
a. Using 鈥測ear鈥� as the independent variable and 鈥淣umber of Family Members Attending College鈥� 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 鈥測ear鈥� as x variable and 鈥淣umber of Family Members Attending College鈥� 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 \(\hat{y}=88.7206-0.0432x\)
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