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Role of retailer interest on shopping behavior. Retail
Chapter 12, Problem 40E(choose chapter or problem)
Role of retailer interest on shopping behavior. Retail interest is defined by marketers as the level of interest a consumer has in a given retail store. Marketing professors at theUniversity of Tennessee at Chattanooga and the Universityof Alabama investigated the role of retailer interest in consumers’ shopping behavior (Journal of Retailing, Summer 2006). Using survey data collected for n = 375 consumers, the professors developed an interaction model for y = willing ness of the consumer to shop at a retailer’s storein the future (called repatronage intentions) as a function of \(x_{1}\) = consumer satisfaction and \(x_{2}\) = retailer interest. Theregression results are shown below.
\(\begin{array}{lrrc}
\hline \text { Variable } & {\hat{\beta}} & t \text {-value } & p \text {-value } \\
\hline \text { Satisfaction }\left(x_{1}\right) & .426 & 7.33 & <.01 \\
\text { Retailer interest }\left(x_{2}\right) & .044 & 0.85 & >.10 \\
\text { Interaction }\left(x_{1} x_{2}\right) & -.157 & -3.09 & <.01 \\
\hline R^{2}=.65, F=226.35, p \text {-value }<.001 &
\end{array}\)
a. Is the overall model statistically useful for predicting y? Test using \(\alpha=.05\).
b. Conduct a test for interaction at \(\alpha=.05\).
c. Use the \(\beta\) estimates to sketch the estimated relationship between repatronage intentions (y) and satisfaction \(\left(x_{1}\right)\) when retailer interest is \(x_{2}\) = 1 (a low value).
d. Repeat part c when retailer interest is \(x_{2}\) = 7 (a highvalue).
e. Sketch the two lines, parts c and d, on the same graph toillustrate the nature of the interaction.
Questions & Answers
QUESTION:
Role of retailer interest on shopping behavior. Retail interest is defined by marketers as the level of interest a consumer has in a given retail store. Marketing professors at theUniversity of Tennessee at Chattanooga and the Universityof Alabama investigated the role of retailer interest in consumers’ shopping behavior (Journal of Retailing, Summer 2006). Using survey data collected for n = 375 consumers, the professors developed an interaction model for y = willing ness of the consumer to shop at a retailer’s storein the future (called repatronage intentions) as a function of \(x_{1}\) = consumer satisfaction and \(x_{2}\) = retailer interest. Theregression results are shown below.
\(\begin{array}{lrrc}
\hline \text { Variable } & {\hat{\beta}} & t \text {-value } & p \text {-value } \\
\hline \text { Satisfaction }\left(x_{1}\right) & .426 & 7.33 & <.01 \\
\text { Retailer interest }\left(x_{2}\right) & .044 & 0.85 & >.10 \\
\text { Interaction }\left(x_{1} x_{2}\right) & -.157 & -3.09 & <.01 \\
\hline R^{2}=.65, F=226.35, p \text {-value }<.001 &
\end{array}\)
a. Is the overall model statistically useful for predicting y? Test using \(\alpha=.05\).
b. Conduct a test for interaction at \(\alpha=.05\).
c. Use the \(\beta\) estimates to sketch the estimated relationship between repatronage intentions (y) and satisfaction \(\left(x_{1}\right)\) when retailer interest is \(x_{2}\) = 1 (a low value).
d. Repeat part c when retailer interest is \(x_{2}\) = 7 (a highvalue).
e. Sketch the two lines, parts c and d, on the same graph toillustrate the nature of the interaction.
ANSWER:Step 1 of 5
(a) \(H_{0}: \beta_{1}=\beta_{2}=\beta_{3}=0\)
Against \(H_{a}\) : attest one \(\beta_{i} \neq 0 \forall_{i}=1,2,3\)
Given results \(F=226.35\)
Rejection region:
\(F>F_{\alpha}\) with 3 and 371 degrees of freedom at \(\alpha=0.05\) level.
\(F_{\alpha}=2.629\)
Here F - calculated value greater than \(F_{a}\)
So we reject \(H_{0}\)
That is, the data provide strong evidence that at least one of the model coefficients
is non-zero. The overall model appears to be statistically useful in predicting
willingness of the consumer to shop at a retailer’s stores in the future.