Question

Imagine that you are a consultant who is building a statistical model to predict how long a customer will remain with a firm (i.e., customer retention). Research demonstrates that both consumer satisfaction and calculated brand commitment should help predict customer retention. Consumer satisfaction is defined as a customer’s overall evaluation of the performance of a product or service to date.78 Calculated brand commitment is a consumer’s dependence on a brand’s benefits due to a lack of choices or switching costs.79 The following table provides data for twenty wireless phone customers. All twenty have used wireless services for 10 years. Column 1 shows the customer number. Column 2 provides consumers’ ratings for overall satisfaction to date on a seven-point scale, where 7 represents the highest rating for satisfaction, and 1 represents the lowest. Column 3 shows consumers’ estimated switching costs, i.e., the cost of switching from their current wireless service provider to a competitor. Finally, column 4 shows how long consumers have been with their current wireless service provider, a surrogate for customer retention.

(1)	(2)	(3)	(4)
Customer Number	Overall Satisfaction (1-7 Scale)	Switching Costs ($)	Months with Firm (Customer Retention)
1	6	120	28
2	4	25	6
3	7	200	48
4	2	20	12
5	5	75	18
6	3	0	2
7	6	50	24
8	4	50	16
9	5	70	20
10	1	0	2
11	6	180	48
12	5	85	20
13	4	80	18
14	2	40	2
15	7	90	48
16	7	110	30
17	1	0	8
18	5	75	12
19	3	60	6
20	6	90	24

1. Conduct a Pearson correlation for (1) switching costs and (2) retention. Recall that a correlation (rxy) measures the extent to which two variables are associated with each other. The value of r always falls between -1 and 1. A positive correlation would indicate that higher switching costs are associated with longer customer retention, whereas a negative correlation would indicate the opposite. A correlation of rxy > 0.75 would be considered large. What is rxy? Does it indicate that higher switching costs are associated with customers' duration with the firm?

2. Conduct a univariate, multiple linear regression analysis using retention as the dependent (y) variable and (1) satisfaction and (2) switching costs as the independent, or predictor (x) variables. Find the data analysis tab and click "regression." Use the third column (retention) for the y-range and the first two columns for the x-range. Click "labels" so that Excel knows the column titles aren't data. Click "new worksheet ply" and provide a name. Then click "OK." Examine the output.

A. Adjusted r-square indicates the proportion of variation in retention explained by satisfaction and switching costs. An adjusted R-Square greater than 0.50 means that satisfaction and switching costs account for more than 50% of the number of months consumers remain with the firm. What is the adjusted R-square in your model? Does it indicate that satisfaction and switching costs explain customer retention?

B. The Satisfaction Coefficient indicates the number of additional months a consumer would remain with his wireless provider if he were to rate the firm one point higher on the 7-point satisfaction scale. According to your model, how many additional months of retention will one satisfaction point bring a wireless provider?

C. Now it's time to predict how long a customer will remain with a wireless provider based on a specific satisfaction score and switching cost. Use 5 as the customer satisfaction score and $100 as the switching cost, and plug these two numbers into your model: intercept coefficient + 5 * satisfaction coefficient + (100) * switching costs coefficient = retention (in months). What is your prediction for how long this particular customer will be retained.

Answer 1

1. The value of Pearson correlation between two variables switching costs and customer retention is 0.8637 which is very large. The value indicates switching costs are highly associated with customer retention.

2. Adjusted R square is 0.781. The value of Adjusted R square indicates that 78.1% of the variability in customer retention is explained by customer satisfaction and switching costs. The model indicates that customer satisfaction and switching costs explains customer retention.

3. The coefficient of customer satisfaction is 0.394. It indicates that with every unit increase in customer satisfaction, customer retention will increase by 0.394 units. If the customer rates one unit higher on customer satisfaction, customer is likely to retain with the same firm for 3.94 months.

4. The equation of regression is calculated from the data given in the question and output from the regression line.

Intercept coefficient + 5 * satisfaction coefficient + (100) * switching costs coefficient = retention (in months)

Substituting the values in above equation we get,

-4.703+5*0.394+100*0.552= 52.467

As per the results obtained, the customer is likely to be retained for 52.467 months.