In: Math
Age | HRS1 |
58 | 32 |
24 | 46 |
32 | 40 |
29 | 40 |
34 | 86 |
49 | 40 |
60 | 40 |
78 | 25 |
39 | 5 |
67 | 15 |
22 | 40 |
Please show work in Excel thank you
Solution:
The required excel output for the regression model is given as below:
Regression Statistics |
||||||
Multiple R |
0.409779396 |
|||||
R Square |
0.167919153 |
|||||
Adjusted R Square |
0.075465726 |
|||||
Standard Error |
19.7139694 |
|||||
Observations |
11 |
|||||
ANOVA |
||||||
df |
SS |
MS |
F |
Significance F |
||
Regression |
1 |
705.8710586 |
705.8710586 |
1.816256659 |
0.210701652 |
|
Residual |
9 |
3497.765305 |
388.6405895 |
|||
Total |
10 |
4203.636364 |
||||
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
|
Intercept |
57.17079946 |
15.97878443 |
3.57791919 |
0.00595008 |
21.02427788 |
93.31732105 |
Age |
-0.446908118 |
0.331611539 |
-1.347685668 |
0.210701652 |
-1.197065534 |
0.303249298 |
Part a
Use t and F to test for a significant relationship between HRS1 and age. Use α = 0.05 and make sure you know what hypotheses you are using to conduct the significance tests.
For the t test for the regression coefficient for age or the slope of the regression model, the p-value is given as 0.2107 which is greater than alpha value 0.05, so we do not reject the null hypothesis. There is not sufficient evidence to conclude that there is a significant relationship between HRSI and age.
For the F test, the p-value is given as 0.2107 which is greater than alpha value 0.05, so we do not reject the null hypothesis. There is not sufficient evidence to conclude that there is a significant relationship between HRSI and age.
Part b
Calculate and interpret the coefficient of determination R2. Based on this R2, did the estimated regression equation provide a good fit? Briefly justify your answer.
The coefficient of determination or the value of R square is given as 0.167919153, this means only 16.79% of the variation in the dependent variable HRSI is explained by the independent variable age.
The estimated regression equation does not provide a good fit.
Part c
Use the estimated regression equation to predict the HRS1 for a 60 year old individual.
Y = 57.17079946 - 0.446908118*x
We are given x=60
Y = 57.17079946 - 0.446908118*60
Y = 30.35631238
Answer: 30.35631238