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# Simple regression using p-value approach

1. Joe's Liquor Store is analyzing its own sales data to determine if the day of the month makes a difference in the volume of liquor sold. For this purpose, 31 single-variable regressions have been run. In Regression 1, daily sales is regressed against a dummy that assigns 1 only to the first day of each month. In Regression 2, daily sales is regressed against a dummy that assigns 1 only to the second day of each month, and so on with the remaining 29 regressions. The p-value of the coefficient of the dummy variable in each of the 31 regressions is tabulated below.

p-value p-value p-value
Regression 1 0.0723 Regression 11 0.1638 Regression 21 0.0402
Regression 2 0.5527 Regression 12 0.1483 Regression 22 0.4939
Regression 3 0.5881 Regression 13 0.5064 Regression 23 0.0848
Regression 4 0.7870 Regression 14 0.9868 Regression 24 0.6972
Regression 5 0.1257 Regression 15 0.1121 Regression 25 0.7370
Regression 6 0.8685 Regression 16 0.0630 Regression 26 0.5289
Regression 7 0.7201 Regression 17 0.4987 Regression 27 0.3290
Regression 8 0.8586 Regression 18 0.9535 Regression 28 0.5607
Regression 9 0.5359 Regression 19 0.8755 Regression 29 0.6275
Regression 10 0.2335 Regression 20 0.7983 Regression 30 0.8996
Regression 31 0.6109
(For example, in Regression 1, the p-value for the dummy variable is 0.0723, where the null hypothesis is that the coefficient is zero).

(a) For this question, do not look at the regression output yet. Suppose that sales are not affected by the day of the month. On average, how many regressions would you expect to show a significant effect at a 5% level?

(b) Look at the regression output. Would you advise the store to change its operating policy, perhaps stocking its store differently on different days, based on the p-values you see?

(c) Suppose Joe had hired consultants and as a part of their presentation, they showed a single one-variable regression indicating that sales are higher on the 7th of each month, with p-value .037. How would you respond? What follow-up question might you ask them?

#### Solution Preview

(a) For this question, do not look at the regression output yet. Suppose that sales are not affected by the day of the month. On average, how many regressions would you expect to show a significant effect at a 5% level?
Since we do not look at the regression output, to expect a significant effect, we need to run all 31 regressions. So 31 regressions are expected.
(b) Look at the regression output. ...

#### Solution Summary

The regression gives detailed steps on analyzing the results of a simple regression using p-value approach.

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