Kohl’s wishes to investigate the relationship between level of advertising, coup
ID: 3235756 • Letter: K
Question
Kohl’s wishes to investigate the relationship between level of advertising, coupon value and sales. Kohl’s advertises several times a month and includes a coupon (in dollars) with each advertisement. The value of the coupon remains the same in a month but varies from month to month. Kohl’s expects that the number advertisements and coupon value have a positive impact on sales. In addition, Kohl’s expects that the impact of advertisements increases as the coupon value increases. Kohl’s collects the sales (in thousands of dollars), number of ads and coupon value for the last one year. The data is in Kohls.sav. Express the model that the company must use, state the null and alternate hypothesis, estimate the model and provide interpretation. When the manufacturer advertises 5 times in a month and includes a $3 coupon, what is the expected sales?
Explanation / Answer
The model is:
y = 0 + 1(X1) + 2(X2) + e
Where,
Y = sales
X1 = Advertisements
X2 = Coupon value
Hypothesis:
H1o: 1 = 0
H1a: 1 > 0
H2o: 2 = 0
H2a: 2 > 0
Here we conduct a Multiple Linear Regression through SPSS. Results of SPSS are given below:
Coefficients
Dependent Variable: Sales in thousands of dollars
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
-7.207
27.585
-.261
.800
Number of Ads
13.248
1.750
.940
7.568
.000
Dollar value of coupon
23.353
7.392
.392
3.159
.012
Interpretation
Coefficients table shows that the parameter (coefficient) for ads is significant P = 0.000. The coefficient for coupon value is also significant (P = 0.012/2 = 0.006) and positive. Hence null hypothesis is rejected and intercept is also not significant.
The model:
y = 0 + 1(X1) + 2(X2) + e
Sales = -7.207 + 13.248 * (x of Ads) + 23.353 * (Dollar value of coupon)
Sales = -7.207 + 13.248 * (5) + 23.353 * (3)
Sales = -7.207 + 66.24 + 70.059
Sales = 129.092 * 1000 = $129,092.00
Coefficients
Dependent Variable: Sales in thousands of dollars
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
-7.207
27.585
-.261
.800
Number of Ads
13.248
1.750
.940
7.568
.000
Dollar value of coupon
23.353
7.392
.392
3.159
.012
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