Question

tion of the equation? 44. The vice-president of United Feeds, Inc., has provided the following quarterly price-quantity data for UF Superb, a horse feed additive. He has asked that the demand equation for this product be estimated. Quarter 1 2 3 4 5 6 7 8 9 10 Price ($) 60 53 43 40 47 57 41 53 37 51 Quantity 83 93 100 10897 80 105 86 110 90 a. Use the ordinary least-squares regression method to estimate this function. b. The firm is considering a price increase to $66. Make a point and 95 percent confidence interval estimate of sales volume if this price increase is carried out. Tires and heef consumption per capita in six cities are as follows:

amswer this question step by step

Answer 1

a).

Consider the given problem here the model is given by, “Q = a + b*P”. Consider the following table.

So, here the estimated regression equation is given by.

2PQ - N*(P bar)*(Q bar) = 45171 - 10*48.2*95.2 = (-715.4) EP^2 - N*(P bar)^2 = 23776 - 10*(48.2)^2 = 543.6 p*g P^2 60 83 4980 3600 5393 4929 2809 4300 1849 4320 1600 4559 2209 4560 3249 105 4305 1681 4558 2809 110 4070 1369 51 90 4590 2601 482 952 45171 23776 48.2 95.2 P Q = 458864 EP^2 = 232324 slope coefficient (b) = (-715.4)/543.6 = (-1.32) Intercept Coefficient (a) = (Q bar) - b*(P bar) = 95.2+1.32*48.2 = 158.82 N = 10 37 TOTAL MEAN

=> Q = 158.82 - 1.32*P.

b).

Now, the upper and the lower limit of the slope coefficient are given by, “(-1.04)” and “(-1.59)”. Similarly, the upper and the lower limit of the intercept coefficient are given by, “171.85” and “145.41” respectively. So, if “P=66”, => the upper limit of “Q” is given by.

=> upper(Q) = 171.85 - 1.04*66 = 103.21. Similarly, the lower limit of “Q” is given by.

=> lower(Q) = 145.41 - 1.59*66 = 40.47.

SUMMARY OUTPUT Regression Statistics Multiple R 0.96953179 R Square 0.939991892 Adjusted R Square 0.932490879 Standard Error 2.740987976 Observations 10 ANOVA df f Regression Residual Total SS 941.4958793 60.10412068 Significance F 3.63411E-06 1 8 MSF 941.4958793 125.3153186 7.513015085 1001.6 Intercept Coefficients Standard Error t Stat P-value 158.6331862 5.732404159 27.67306383 3.13697E-09 -1.316041207 0.117562119 -11.19443248 3.63411E-06 Lower 95% Upper 95% Lower 95.0% Upper 95.0% 145.4142385 171.8521339 145.4142385 171.8521339 -1.58713994 -1.044942474 -1.58713994 -1.044942474

So, here the 95% confidence interval of the slope coefficient is given by, “(-1.32) +/- SE(b)*t(0.025,8)”, “(-1.32) +/- 0.1176*2.306”. Similarly, the 95% confidence interval of the intercept coefficient is given by, “158.82 +/- SE(a)*t(0.025,8)”, “158.82 +/- 5.7324*2.306”.