I am interested in determining whether there is a relationship between number of

Question

I am interested in determining whether there is a relationship between number of packs of cigarettes smoked per day and longevity (in years). Please look at the output of regression below and give short answers the following questions

a. Is this regression significant? Why?

b. What is the coefficient of correlation? Interpret the coefficient of correlation

c. What is the coefficient of determination? What can you say about the relationship between two variables?

d. What is the regression equation?

e. Interpret the Y-intercept of the linear equation

f. Interpret the slope of the linear equation

g. What is the test-statistic to test the significance of the slope? What is your conclusion? (5% significance level)

h. What is the test-statistic to test the significance of the coefficient of correlation? What is your conclusion? (5% significance level)

i. How long will one live who smokes 2.5 packs per day?

Multiple R R Square Adjusted R Square Standard Error 0.875178878 0.785938069 0.736680328 3.802137557 ANOVA df MS 378.45 115.65 378.45 26.17898833 14.45625 0.000911066 Residual Total Intercept X Variable1 2.082516507 36.20619561 3.71058E-10 5.11654066 0.000911066 75.4 70.59770522 80.20229478 4.35 6.310528635 -2.389471365

Explanation / Answer

Answers to the questions is as follows:

a. The regression is significant because the Significance value of F in the ANOVA table is .0009 which is less than .05

b. The correlation coefficient is .8752, as seen in the regression statistics. It means that a strong relation exists between the dependent and independent variable

c. Coefficient of determination is .7659, which means that 76.59% of variance in dependent variable is explained by predictor variable

d. Regression equation is : Y^ = 75.4 -4.35X

e. It means that if a person doesn't smoke ciggys pack at all, i.e. X=0, then he will live for Y^ = 75.4 -4.35*0 = 75.4 years

f. The slope of -4.35 means that per ciggy pack smoked , the longevity comes down by 4.35 years.

g. The test statistic is -5.1165. Conclusion: it brings a p-value of .0009 which is less than .05, impying significant slope

h. df is n-2 = 8, at .05 alpha according to correaltion table the critical correlation is .631. Our corelation is at .875 , more than .631, i.e.
our correlation at alpha = .05 is significant

i. If one smokes X = 2.5 ciggy pack per day then one will live = 75.4 -4.35*2.5 = 64.525 years

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