Homework Sourse1 The following data represent the age in years of various p
1. The following data represent the age (in years) of various people and the number of days per week they exercise. We are interested in doing a regression analysis on this data to see if age affects how many days per week someone works out.
Age Days they Exercise
24 4
18 6
29 6
17 4
61 5
51 2
30 6
24 4
18 2
21 1
a. Which one is the independent variable and which one is the dependent variable?
b. Find b0.
c. Find b1.
d. Find SST.
e. Find SSR.
f. Find SSE.
g. Find the coefficient of determination.
h. Find the correlation coefficient.
i. Find s^2.
j. Find the test statistic for testing if b1 is significant or not.
k. What conclusion would you make based on the test statistic found above?
l. Find the 95% confidence interval for B1.
m. Assuming a person is 40 years old, how many days per week are they expected/predicted to exercise?
n. Assuming a person is 40 years old, what is the 90% confidence interval for the expected number of days of exercise for them?
o. Assuming a person is 40 years old, what is the 90% prediction interval for the expected number of days of exercise for them?
Solution
The following data represent the age (in years) of various people and the number of days per week they exercise. We are interested in doing a regression analysis on this data to see if age affects how many days per week someone works out.
Regression Analysis
r²
0.003
n
10
r
0.057
k
1
Std. Error
1.933
Dep. Var.
days
ANOVA table
Source
SS
df
MS
F
p-value
Regression
0.0976
1
0.0976
0.03
.8756
Residual
29.9024
8
3.7378
Total
30.0000
9
Regression output
confidence interval
variables
coefficients
std. error
t (df=8)
p-value
90% lower
90% upper
Intercept
3.7957
1.4042
2.703
.0269
1.1846
6.4069
age
0.0070
0.0431
0.162
.8756
-0.0733
0.0872
Predicted values for: days
90% Confidence Interval
90% Prediction Interval
age
Predicted
lower
upper
lower
upper
Leverage
40
4.075
2.650
5.499
0.208
7.942
0.157
a. Which one is the independent variable and which one is the dependent variable?
independent variable = age
dependent variable = number of exercise days per week
b. Find b0. 3.7957
c. Find b1. 0.007
d. Find SST. 30
e. Find SSR. 0.0976
f. Find SSE. 29.9024
g. Find the coefficient of determination. 0.003
h. Find the correlation coefficient. 0.057
i. Find s^2. 1.933
j. Find the test statistic for testing if b1 is significant or not. t=0.162
k. What conclusion would you make based on the test statistic found above?
Calculated t=0.162, p=0.8756 >0.05, not significant.
Age is not significantly predicting exercise days.
l. Find the 95% confidence interval for B1. (-0.0733, 0.0872)
m. Assuming a person is 40 years old, how many days per week are they expected/predicted to exercise?
Predicted days =4.075
n. Assuming a person is 40 years old, what is the 90% confidence interval for the expected number of days of exercise for them?
90% CI =(2.650, 5.499)
o. Assuming a person is 40 years old, what is the 90% prediction interval for the expected number of days of exercise for them?
90% PI =(0.208, 7.942)
| Regression Analysis | ||||||
| r² | 0.003 | n | 10 | |||
| r | 0.057 | k | 1 | |||
| Std. Error | 1.933 | Dep. Var. | days | |||
| ANOVA table | ||||||
| Source | SS | df | MS | F | p-value | |
| Regression | 0.0976 | 1 | 0.0976 | 0.03 | .8756 | |
| Residual | 29.9024 | 8 | 3.7378 | |||
| Total | 30.0000 | 9 | ||||
| Regression output | confidence interval | |||||
| variables | coefficients | std. error | t (df=8) | p-value | 90% lower | 90% upper |
| Intercept | 3.7957 | 1.4042 | 2.703 | .0269 | 1.1846 | 6.4069 |
| age | 0.0070 | 0.0431 | 0.162 | .8756 | -0.0733 | 0.0872 |
| Predicted values for: days | ||||||
| 90% Confidence Interval | 90% Prediction Interval | |||||
| age | Predicted | lower | upper | lower | upper | Leverage |
| 40 | 4.075 | 2.650 | 5.499 | 0.208 | 7.942 | 0.157 |
