Question

Supermarkets can use the scanning data collected at the checkout counters to evaluate the effect of price on the sales of any product. Weekly data was collected on a particular beverage brand, including sales (in number of units) and price (in dollars). Based on a simple linear regression analysis, the fitted regression equation was: Y = 2259 - 1418 X. The ANOVA F-statistic was 60.52 with the p-value of <0.0001, and R² = 0.597.  According to this model, is the explanatory variable (X) a good predictor of the response variable (Y)?

	A.	Yes, the intercept is very large.
	B.	No, the slope is negative.
	C.	No, R2 is too small.
	D.	Yes, the p-value associated with the F-statistic is very small

Answer 1

If we want to test theexplanatory variable (X) a good predictor of the response variable (Y)

We use decision rule

Decision rule : if p-value < a we reject the null hypothesis otherwise we fail to reject the null hypothesis

Our p-value = 0.0001 < 0.05 or 0.01

So p-value associated with the F statistic is very small

Yes , p-value associated with the F statistic is very small.