Question

Sample Data for Supermarket Profits. Supermarket Food Sales Nonfood Sales Store Size Profit Number (tens of thousands (tens of thousands(thousands of (thousands of dollars) square feet) X. 35 of dollars) of dollars) 35 98 83 76 93 20 15 17 305 130 189 175 101 269 421 195 282 203 27 16 28 46 56 12 40 16 27 57 31 92 ?? 10 23

Run an excel data analysis for regression

A) What is the F test and interpret it

B) Run a T Test and interpret it

C) Use the hypothesis equation to see if you if you accept or reject the hypothesis

Answer 1

A) Using Excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.992398792
R Square	0.984855361
Adjusted R Square	0.977283042
Standard Error	1.249867779
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	3	609.5269832	203.1756611	130.0599363	7.55516E-06
Residual	6	9.373016791	1.562169465
Total	9	618.9
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-10.17024332	3.473128593	-2.928265696	0.026346428	-18.66868281	-1.671803818
X1	0.027038115	0.012040996	2.245504802	0.065846812	-0.002425142	0.056501372
X2	0.097052345	0.030147122	3.219290578	0.018153389	0.023284996	0.170819694
X3	0.524675168	0.059158249	8.869011174	0.000114333	0.379920149	0.669430187

F test:

$H_0:\beta _1=\beta _2=\beta _3= 0$

$H_a:\beta _1\neq \beta _2\neq \beta _3\neq 0$

The test statistic: F= 130. 0599

P-value= 0.000007

The test statistic is significant and rejects H0. There is enough evidence to support the claim that there is significant relationship with output variable.

B) T- test and interpret:

	Coefficients	Standard Error	t Stat	P-value
Intercept	-10.17024332	3.473128593	-2.928265696	0.026346428
X1	0.027038115	0.012040996	2.245504802	0.065846812
X2	0.097052345	0.030147122	3.219290578	0.018153389
X3	0.524675168	0.059158249	8.869011174	0.000114333

To interpret coefficients:

For every additonal unit of X1, output value increases by 0.027038115 unit

For every additional unit of X2, output value increases by 0.097052345 units

For every additonal unit of X3, output value increases by 0.524675168 units.

Hypothesis test:

$H_0:\beta = 0$

$H_a:\beta \neq 0$

The test statistic: $t= \frac{b_i-\beta _i}{S_b_i}$

t(x1)= 2.2455 and P-value= 0.066

t(x2)= 3.2199 and p-value= 0.018

t(x3)= 8.8690 and p-value= 0.00014

C) Hypothesis tests:

The test statistic: $t= \frac{b_i-\beta _i}{S_b_i}$

t(x1)= 2.2455 and P-value= 0.066

t(x2)= 3.2199 and p-value= 0.018

t(x3)= 8.8690 and p-value= 0.00014

At 0.05 significant level, X1 is not significant and X2, X3 are significant and good for prediciton.

X1- failed to reject H0

X2- Reject Ho

X3- Reject H0