Homework 9
Solution
Page 428 # 14
(a)
Scatter plot
(b) Correlation coefficient
r = -0.8312962
(c) There is a strong negative linear correlation between the number of hours of TV watched and the test scores of students.
Page 430 # 28
(a) H0: ρ = 0
Ha: ρ ≠ 0
(b) t0 = ± 1.812
(c) 
(d) Reject H0. There is enough evidence to conclude that a significant linear relationship between the two variables exists.
Page 438 #14
Equation of the regression line:
Scatter plot with regression line:
Predict values for y. Are they meaningful?
|
x |
Predicted y
value |
Meaningful? |
|
4 |
77.70 |
Yes |
|
8 |
61.43 |
Yes |
|
9 |
57.36 |
Yes |
|
15 |
32.96 |
No. x= 15 is outside the range of the data, so it is not meaningful to make predictions for y for that x value. |
Page 440 #22
Since x = 80, which is outside the range of the data, a prediction for y is not meaningful. We have no information beyond x = 44; x = 80 is far outside the range of the data.
Page 449 #10
|
x |
y |
|
|
|
|
|
|
|
525 |
164 |
163.124 |
-41.7143 |
1740.082 |
-42.5903 |
1813.93244 |
.767376 |
|
510 |
179 |
186.149 |
-26.7143 |
713.6531 |
-19.5653 |
382.800405 |
51.1082 |
|
500 |
206 |
201.499 |
0.285714 |
0.081633 |
-4.21529 |
17.7686337 |
20.259 |
|
485 |
196 |
224.524 |
-9.71429 |
94.36735 |
18.80971 |
353.805352 |
813.6186 |
|
486 |
220 |
222.989 |
14.28571 |
204.0816 |
17.27471 |
298.415754 |
8.9341 |
|
487 |
231 |
221.454 |
25.28571 |
639.3673 |
15.73971 |
247.738606 |
91.1261 |
|
487 |
244 |
221.454 |
38.28571 |
1465.796 |
15.73971 |
247.738606 |
508.3221 |
|
|
|
|
|
4857.429 |
|
3362.19979 |
1494.136 |
(a) 
69.2% of the variation in cigarettes exported by the US can be explained by the variation in the number of cigarettes consumed in the US.
(b) 
The standard deviation of the number of cigarettes exported for a specific number of cigarettes consumed is about 17,285,000,000.
Page 450 #18
The formula for the prediction interval is:
We can say with 95% confidence that the number of cigarettes exported when 490 billion are consumed will be between 168,435,400,000 and 264,926,600,000.
Page 456 #6
Given in the output from Minitab on the homework assignment sheet are:
R2=.998
se=0.1924
The standard deviation of the predicted equity given a specific net sales and total assets is $0.1924 billion. The multiple regression model explains 99.8% of the variation in y.