4. The data below represent Y, sales in thousands of dollars; X1, price in cents
ID: 3236683 • Letter: 4
Question
4. The data below represent Y, sales in thousands of dollars; X1, price in cents; X2, promotion in dollars.
Sales Price Promotion
53 674 3250
59 628 3589
61 536 4266
63 521 4875
65 528 4912
71 506 5763
76 453 6173
83 399 6369
a) Give the equation of the regression line. Round to 3 decimal places.
b) Give the value of the slope for price
c) Interpret its meaning in the context of this problem. Move ethe decimal appropriately
d) Give the value of the slope for promotion.
e) Interpret its meaning in the context of this problem. Move the decimal appropriately.
f) Predict sales for price of $4.50 and $6000 spent on promotion. Move the decimal appropriately.
g) Give the calculated F for testing if the relationship is significant between sales & price and promition.
h) What is its p-value?
i) Is the relationship significant? Please answer yes or no.
j) Give the coefficient of determination.
k) Interpret its meaning in the context of this problem.
l) Give the coefficient of partial determination for price. Show your calculations.
m) Interpret its meaning in the context of this problem.
n) Give the coefficient of partial determination for promotion. Show your calculations.
o) Interpret its meaning in the context of this problem.
Explanation / Answer
(a) y = 57.790 - 0.035x1 + 0.006x2
(b) Slope = -0.035
(c) The sales decrease by $35 per 1 cent increase in the price
(d) Slope = 0.006
Regression Analysis R² 0.932 Adjusted R² 0.904 n 8 R 0.965 k 2 Std. Error 3.017 Dep. Var. y ANOVA table Source SS df MS F p-value Regression 620.3643 2 310.1821 34.08 .0012 Residual 45.5107 5 9.1021 Total 665.8750 7 Regression output confidence interval variables coefficients std. error t (df=5) p-value 95% lower 95% upper std. coeff. Intercept 57.7900 0.000 x1 -0.0351 0.0443 -0.792 .4644 -0.1490 0.0788 -0.316 x2 0.0056 0.0034 1.648 .1602 -0.0031 0.0142 0.658Related Questions
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