Question

:///Users/haphan/Downloads/Example%20a.pdf Model A A 10-year study conducted by AHA provided data on how age and blood pressure relate to the risk of strokes. SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.77 0.59 10.08 20 ANOVA MSF Regression Residual Total 17 1728.639722 19 Coefficientsa Error tStat P-value Intercept -77.98 1.07 0.21 21.58-3.61 0.0021 4.44 0.0004 2.68 0.0158 0.24 0.08 Blood Pressure Find the adjusted coefficient of determination How many independent variables are significant at the 5% level of significance assuming we are engaged in a two tailed analysis? (Which one is/is not ) Find the F test statistic Show steps According to the estimated regression equation If Age-55; Blood Pressure 150; The numeric value for Risk equals. Amazon.com Bonus Rewards are ea Consider adding two independent variables to the model developed in part (A), one for the interaction between age and blood-pressure level and the other for whether the person is a smoker (B) SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error 0.838 0.702 0.623 9.120 20 ANOVA Significance MS 0.00071 Regressior Residual Total 2943.254735.813 1247.696 4190.950 8.846 15 19 83.180 Coefficients Standord ErrorStotP-value Intercept Age -31.205 0.387 77.891 1.145 0.401 0.6943 0.7400 0.338 com Bonus file://users/haphan/Downloads/Example%20a.pdf Regression Statisties M. -ole R R Square Adjusted R Square Standard Error Observations 0.838 0.702 0.623 9.120 20 ANOVA Significance MS 4 2943.254 735.813 83.180 8.846 0.00071 Regression Residual Total 15 19 1247.696 4190.950 Coefficients Standard Error tStat P-value Intercept Age Blood Pressure Smoker Age Blood Pressure 31.205 0.387 -0.079 10.193 77.891 1.145 0.531 4.399 0.401 0.6943 0.338 0.7400 0.149 0.8835 2.317 0.0351 0.004 0.008 0.466 o 0.6481 At a.01 level of significance, test to see whether the addition of the interaction term and the smoker variable (Regression B) contribute significantly to the estimated regression equation developed in part (A). Show all steps com. Bonus

Answer 1

Model A related question have been solved completely.

Anova table

The formulas for the ANOVA table are given below.

To find SST

Anova Table Prob >F df DFM- p SSM DFE = n-p-ISSE DFT = n-1 SST ms F stat Model Error Total MSM-SSM/DFM Fstat MSM/MSE F(p, n-p-1) | MSE= SSE/DFE p is the no. of independent variables in the model n is the no. of observations DFM is the degree of freedom of model DFE is the degree of freedom of error DFT is the degree of freedom of total SSM is the sum of square of model SSE is the sum of square of model MSM is mean square of model MSE is the mean square Error

$Rsquare = 1 - \frac{SSE}{SST}$

From the output given we have

Rsquare = 0.59
SSE = 1728.639722

$\\Rsquare = 1 - \frac{SSE}{SST} \\ 0.59 = 1 - \frac{1728.639722}{SST} \\\\\\ SST = \frac{1728.639722}{1- 0.69} = 5576.257168\\$

a. Adjusted R2

$\\Adjusted.R^2 = 1 - (1-R^2)\frac{n-1}{n-(k+1)}\\\\ \text{we are given}\\ \text{n = no. of observation, k = no. of variable.}\\ n = 20\\ k = 2\\ R^2 = 0.59\\ \text{Putting these values in the above equation we get}\\\\ Adjusted.R^2 = 1 - (1-R^2)\frac{n-1}{n-(k+1)}= 1 - (1-0.59)\frac{20-1}{20-(2+1)}=0.633157895$

b. Significant independent variables.
To check if a variable is signficant we need to check the pvalue corresponding to that variable.

If the pvalue is less than 0.05, than the variable is significant.

From the pvalue we see that all the variable has a pvalue less than 0.05, hence all the variable(age, blood pressue) are signficant.

c.

The regression equation is

risk = -77.98 + 1.07 Age + 0.21 Blood pressure

We are given AGe = 55, BP = 150,

Put these values we get

risk = -77.98 + 1.07 (55)+ 0.21 (150)= 12.37