Question

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.[3.5 points]

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. Hint: If you used Excel Regression Tool to answer part c, R²was reported with your output.  [2.5 points]

3. Use the estimated regression equation to predict the HRS1 for a 60 year old individual.

[1.5 points]

Age	HRS1
58	32
24	46
32	40
29	40
34	86
49	40
60	40
78	25
39	5
67	15
22	40

Answer 1

Answer Date: 11/11/2019 To test the hypothesis is that there is a significant relationship between HRS1 and age at 5% significance level. The null and alternative hypothesis is, Ho:B2 = 0 Ha:B, 70 The t-test statistics is, By using Excel software, find t-test statistics with help of following steps: 1) Import the data. 2). Select Data Analysis from Data menu. Select Regression and click OK. Input Y Range and Input X range. Click Ok.

SUMMARY OUTPUT Regression Statistics Multiple R 0.409779396 R Square 0.167919153 Adjusted R Square 0.075465726 Standard Error 19.7139694 Observations ANOVA df 1 Regression Residual Total SS M SF Significance F 705.8710586 705.8711 1.816257 0.210701652 3497.765305 388.6406 4203.636364 9 10 Intercept Age Coefficients 57.17079946 -0.446908118 Standard Error Stat p-value Lower 95% Upper 95% 15.97878443 3.577919 0.00595 21.02427788 93.31732105 0.331611539 -1.347686 0.210702 -1.19706553 0.303249298 From the Excel output, the t-test statistics is -1.35 The p-value for this test is, From the Excel output, the p-value for this test is 0.2107).

Decision The conclusion is that the p-value in this context is higher than 0.05 which is 0.2107, so the null hypothesis is not rejected at 5% level of significance. There is insufficient evidence to indicate that there is a significant relationship between HRS1 and age. The result is not statistically significant. To test the hypothesis is that the overall regression model of HRSi (y) on age (x) is significant at 5% significance level. The null and alternative hypothesis is, H:B. = 0 H.:B, 70 The F-test statistics is, From the Excel output, the F-test statistics is 1.82).

The p-value for this test is, From the Excel output, the p-value for this test is 0.2107) Decision The conclusion is that the p-value in this context is higher than 0.05 which is 0.2107, so the null hypothesis is not rejected at 5% level of significance. There is insufficient evidence to indicate that the overall regression model of HRSI () on age (x) is significant. The result is not statistically significant. The coefficient of determination (R-squared) is, From Excel output in part (a), the coefficient of determination (R-squared) is 0.1679 Interpretation of coefficient of determination

R= 0.1679. 16.79% of sample variation in HRS1 (v) can be explained by the model containing age. The estimated regression equation does not provides a good fit due to the coefficient of determination (R-squared) is 16.79% is very small. The estimated regression equation to predict the HRS1 for a 60 year old individual is, y = Be + B. x = 57.171 -0.447x (From Excel outptu in part(a)) = 57.171 -0.447 x 60 = 30.36 The estimated regression equation to predict the HRS1 for a 60 year old individual is 30.36