The Federal Trade Commission measured the number of milligrams of tar and carbon

Question

The Federal Trade Commission measured the number of milligrams of tar and carbon monoxide (CO) per cigarette for all domestic cigarettes. Let x and y equal the measurements of tar and co, respectively, for 100 millimeter filtered and mentholated cigarettes. A sample of 12 brands yielded the following data: Find point estimates for beta_0, beta_1, and sigma_2 and find the least squares regression line for these data. Test the hypotheses H_0: beta_1 = 0 at the alpha = 0.05 Calculate 95% confidence interval for the parameter Find a 95% confidence interval for the mean of Y when x = 5, 15. Find a 95% prediction interval for a new Y when x = 5, 15. Calculate the correlation coefficient between x and y. Test the hypothesis that the population correlation coefficient rho between x and y is 0 vs. the alterative that rho notequalto 0.

Explanation / Answer

(a) b0 = 2.5753, b1 = 0.8191, Standard error = 1.988

The regression equation is y = 2.5753 + 0.8191x

(b) p- value for the slope coefficient is 0.0001 (< 0.05). So we conclude that 1 0

(c) The 95% confidence interval for 1 is [0.5242, 1.1139]

(d) For x = 5, the 95% confidence interval for mean y is [4.897, 8.444]

For x = 15, the 95% confidence interval for mean y is [12.718, 17.005]

Regression Analysis r² 0.793 n   12 r   0.890 k   1 Std. Error   1.988 Dep. Var. y ANOVA table Source SS   df   MS F p-value Regression 151.3886 1   151.3886 38.30 .0001 Residual 39.5281 10   3.9528 Total 190.9167 11   Regression output confidence interval variables coefficients std. error    t (df=10) p-value 95% lower 95% upper std. coeff. Intercept 2.5753 0.000 x 0.8191 0.1323 6.189 .0001 0.5242 1.1139 0.890 Predicted values for: y 95% Confidence Intervals 95% Prediction Intervals x Predicted lower upper lower upper Leverage 5 6.671 4.897 8.444 1.899 11.442 0.160 15 14.861 12.718 17.005 9.940 19.782 0.234

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