Consider the following data concerning the demand (y) and price (x) of a consume

Question

Consider the following data concerning the demand (y) and price (x) of a consumer product.

Demand, y 255 243 249 236 239 225 Price, x $ 2.06 $ 2.21 $ 2.49 $ 2.61 $ 2.87 $ 2.99

(a) From the given plot, does it seem reasonable to use the simple linear regression model to relate y to x? No Yes

(b) Calculate the least squares point estimates of the parameters in the simple linear regression model. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.) b0 b1

(d) Test the significance of the regression relationship between y and x. p-value = .000 H0, relationship is significant

(e) Find a point prediction of and a 95 percent prediction interval for the demand corresponding to each of the prices $2.10, $2.75, and $3.10. (Round your x0 answers to 2 decimal places and other answers to 3 decimal places.) x0 Point prediction Prediction interval [__ans5__, ] [, ] [, ]

Explanation / Answer

(a) Yes (b) SUMMARY OUTPUT Regression Statistics Multiple R 0.841284 R Square 0.707758 Adjusted R Square 0.634698 Standard Error 0.219271 Observations 6 ANOVA df SS MS F Significance F Regression 1 0.465764 0.465764 9.687304 0.035787 Residual 4 0.192319 0.04808 Total 5 0.658083 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 9.563878 2.259018 4.233643 0.013331 3.291837 15.83592 3.291837 15.83592 y -0.02913 0.00936 -3.11244 0.035787 -0.05512 -0.00314 -0.05512 -0.00314 x = 9.56 - 0.029y b0 =9.56 b1 = -0.029 (d) p value = 0.03, reject Ho at 5% level of significance

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