Question

Tiffany Dolsing, a market analyst at the market research firm of Sanders & Sons, is analyzing household budget data collected by her firm. Tiffany’s dependent variable is monthly household expenditures on groceries (in $'s), and her independent variable is annual household income (in $1,000's). Regression analysis of the data yielded the following tables.

	Coefficients	Standard Error	t Statistic	p-value
Intercept	39.14942	22.30182	1.755436	0.109712
x	1.792312	0.407507	4.398234	0.001339

Source	df	SS	MS	F		s.e. = 29.51443
Regression	1	16850.99	16850.99	19.34446		r2 = 0.682478
Residual	9	7839.915	871.1017
Total	10	24690.91

Using α = 0.05, Tiffany should ________________.

Answer 1

here we want to test the null hypothesis H0:=0 and alternate hypothesis Ha:

since the critical F(0.05,1,9)=5.12 is less than calculated F=19.34, so we reject H0 and conclude that regression coefficient is not zero and conclude that independent variable annual household income is significantly explaining the variability in dependent variable monthly household expenditures on groceries.

Also p-value=0.0013 of the the slope is less than alpha-0.05, so there is significant association/correlation between dependent and independent variable