Question

What affects 4K Ultra HD Smart TV sales?

TVs are sold through a variety of outlets such as large electronics stores, department stores, large discount chains and online.

Sales figures (number of units) for the Samsung 7 Series were obtained for last quarter from a sample of 30 different stores.

Also collected were data on the selling price and amount spent on advertising the Samsung 7 Series (as a percentage of total advertising expenditure in the previous quarter) at each store (please find a data set below)

Sales (number of units)	Price ($)	Advertising (% from budget)
70	1800	10
90	1800	20
120	1800	26
84	1850	18
66	1900	15
71	1890	13
98	1945	23
110	1910	30
119	1910	25
52	2000	5
108	2000	20
109	2010	30
105	2010	21
41	2100	8
67	2110	11
69	2120	15
68	2200	16
75	2210	17
80	2199	17
100	2205	22
63	2300	13
81	2350	20
39	2400	12
49	2400	10
55	2410	6
41	2450	9
35	2450	10
32	2460	15
35	2500	7
58	2500	12

a. Write out the estimated regression equation. (2 points)

b. Is the regression equation significant overall (for the entire model)? Explain. (2 points)

c. How much of the variability in Sales is explained by the regression equation? (2 points)

d. State the hypotheses for testing the regression coefficient of Price. Based on the results, what do you conclude at α = 0.05? (2 points)

e. State the hypotheses for testing the regression coefficient of Advertising Expenditure. Based on the results, what do you conclude at α = 0.05? (2 points)

f. Predict the sales for a store that sells the Samsung 7 Series for $2299 and spends 9% of its advertising budget on the product. (2 points)

Answer 1

The analysis is done in Minitab

The output is:

Regression Analysis: Sales versus Price, Advertising

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 2 17647 8823.6 78.09 0.000
Price 1 1750 1750.4 15.49 0.001
Advertising 1 7725 7724.7 68.36 0.000
Error 27 3051   113.0
Total 29 20698

Model Summary

S R-sq R-sq(adj) R-sq(pred)
10.6299 85.26% 84.17% 81.78%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 110.3 23.9 4.61 0.000
Price -0.03806 0.00967 -3.94 0.001 1.34
Advertising 2.781 0.336 8.27 0.000 1.34

Regression Equation

Sales = 110.3 - 0.03806 Price + 2.781 Advertising

Fits and Diagnostics for Unusual Observations

Obs Sales Fit Resid Std Resid
28 32.00 58.40 -26.40 -2.63 R

R Large residual

a) The estimated regression equation is

Sales = 110.3 - 0.03806 Price + 2.781 Advertising

b) From the ANOVA table , the p-value for the regression is 0.000

Hence the regression equation is significant overall.

c) R square = 85.26%

85.26% of the variability in Sales is explained by the regression equation.

d)

beta1 is the coeffecient of price in the regression model.

From the table of coeffecients, the p value for the coeffecient of price is 0.001<0.05

Hence the coeffecient of price is significant.

e)

beta2 is the coeffecient of Advertising Expenditure in the regression model.

From the table of coeffecients, the p value for the coeffecient of price is 0.000<0.05

Hence the coeffecient of Advertising Expenditure is significant.

f) the sales for a store that sells the Samsung 7 Series for $2299 and spends 9% of its advertising budget on the product is:

Sales = 110.3 - 0.03806 *2299 + 2.781 *9 = 64.382 ~ 64 units