Given the following data on a question discussing if the age of a person and the

Question

Given the following data on a question discussing if the age of a person and the number of siblings he/she has influence the number of cans of soda consumed per week? There are 3 variables Age, # of siblings, and soda cans per week. Data: Age: 47,32,18,34,23,21,20,20,38,19,19,22,23,23,20,23 # of Siblings: 3,1,3,4,3,3,0,1,5,1,6,2,2,4,2,4 Soda Cans Per week: 5,10,5,2,10,11,2,2,2,1,12,15,2,0,1,8 Question 1: Write the Regression Model. Question 2: Write the prediction equation and illustrate how to use it with an example. Also interpret the Betas Question 3: Discuss the ANOVA table found in your output Question 4: Interpret S and R2 Question 5: Conduct the Analysis of Variance F-test to determine if your model is useful in predicting y Question 6: Which variables are significant? Look at the p-values for the Betas. Question 7: What are your conclusions?

Explanation / Answer

answers

1)cans=intercept+beta1*age+beta2*siblings

2)cans=5.7663-0.08320*age+0.6633*siblings , for given value of age and sibling we can calculate number of cans per weeks e.g. if age is 40 and siblings are 2 then

estimated cans per week=5.7663-0.08320*40+0.6633*2=3.7649

3) from Anova table F-statistic of the model is 0.38 and its p-value is 0.6885

4)R2=0.0558, which is proportion of the variation in dependent variable explained by independent variables age and siblings

5)F-statistic of the model is 0.38 and its p-value is 0.6885 and it is not significant at 5% level of significance and not useful to predict y

6)none of the regression coefficient of age and siblings are significant as the p-value is more than alpha=0.05

7)model is not fitting well and not useful to predict the dependent variable

3)anova table

Analysis of Variance Source DF Sum of
Squares Mean
Square F Value Pr > F Model 2 19.08549 9.54274 0.38 0.6885 Error 13 322.91451 24.83958 Corrected Total 15 342.00000

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