Question

In: Math

Use t and F to test for a significant relationship between HRS1 and age. Use α...

  1. 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.
  2. 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, R2 was reported with your output.
  3. Use the estimated regression equation to predict the HRS1 for a 60 year old individual.
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

Solutions

Expert Solution

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


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