Question

The marketing manager of a large supermarket chain would like to determine the effect of shelf space (in feet) on the weekly sales of international food (in hundreds of dollars). A random sample of 12 equal –sized stores is selected, with the following results: Store Shelf Space(X) Weekly Sales(Y) 1 10 2.0 2 10 2.6 3 10 1.8 4 15 2.3 5 15 2.8 6 15 3.0 7 20 2.7 8 20 3.1 9 20 3.2 10 25 3.0 11 25 3.3 12 25 3.5 Based on these data, what are the least squares regression coefficients of the Y-intercept (a) and slope (b)? Place your answers, rounded to 3 decimal places , in the blanks provided.

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 1.48 + 0.074 x
Sample size: 12
R (correlation coefficient) = 0.82700064
R-sq = 0.68393006
Estimate of error standard deviation: 0.30805844

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	1.48	0.29224989	? 0	10	5.0641593	0.0005
Slope	0.074	0.015908069	? 0	10	4.6517273	0.0009

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	2.0535	2.0535	21.638567	0.0009
Error	10	0.949	0.0949
Total	11	3.0025

Hence,

a = 1.48

b = 0.074