4. A random sample of 6 states gave the following figures for annual per capital

Question

4. A random sample of 6 states gave the following figures for annual per capital cigarette consumption and annual death rate per 100,000, from lung cancer: State Delaware Indiana Iowa Montana New Jersey Washington Cigarette Consumption 2200 2600 2100 2400 2900 2100 Death rate per 100,000 24 24 24 24 23 24 (a) At 5% level of significance, do you think the cigarette consumption holds the explanatory power on the chance of getting lung cancer? (b) How well does the regression model explain the chance of getting lung cancer? (c) Do you observe any potential problems in the data and in the model? How would you propose to improve the experiment? Please be specific.

Explanation / Answer

a)

H0: =0 (no linear relationship)

H1: at least one i 0   (Independent variable affects Y)

F=6.82 and F Crit is 0.06 and since F>F Crit, reject the null hypothesis. Thus, we conclude that independent variable affects Y

b)

r^2 is 0.6302 which means that 63.02% of variation in dependent variable is accounted for by the independent variable.

c)

Here, we can see that we just have one independent variable and that too is not significant (p-value=0.06). Hence, better it would be to increase the size of the dataset so that we get more robust estimates and better p-value and significant variables.

SUMMARY OUTPUT Regression Statistics Multiple R 0.79 R Square 0.63 Adjusted R Square 0.54 Standard Error 0.28 Observations 6 ANOVA df SS MS F Significance F Regression 1 0.53 0.53 6.82 0.06 Residual 4 0.31 0.08 Total 5 0.83 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 26.26 0.93 28.09 0.00 23.66 28.85 Cigarette Consumption 0.00 0.00 -2.61 0.06 0.00 0.00

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