Question

You estimate the demand function for soft drinks using a multiple regression model. The MS Excel printout for the regression follows:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.835478305
R Square	0.698023997
Adjusted R Square	0.677434724
Standard Error	38.26108281
Observations	48
ANOVA
	df	SS	MS	F	Significance F
Regression	3	148889.8565	49629.95217	33.9023141	1.64557E-11
Residual	44	64412.06016	1463.910458
Total	47	213301.9167
	Coefficients	Standard Error	t Stat	P-value
Intercept	514.2669369	113.3315243	4.537721874	4.36383E-05
6 pack price	242.9707509	43.52628127	5.582161944	1.38245E-06
mean temp	2.931228055	0.711458375	4.120027476	0.000164543
income/capita	1.224163793	1.522612776	0.803988914	0.425725939

1. Interpret the estimated regression coefficient of mean temperature.
2. What is the probability, if the true value of the regression coefficient of disposable income is zero, that the t statistic is as large (in absolute terms) as we observe? What does this mean?

Answer 1

Answer

(a)

We can see from above table that regression coefficient of mean temperature is 2.931 and also p value < 0.05 implies that temperature is significant and thus we have the following interpretation :

Increase in mean temperature by 1 units(can be any celcius, kelvin etc depending on the notation discussed in the data) will result in increase in demand soft drinks by 2.931 units(depending on the notation discussed in the data).

(b)

We can see from above regression result that P value for income is 0.425. This means that if null is true(i.e. income = 0) Probability of getting t statistic greater than or equal to 0.80 is 0.425.

Hence, Probability = 0.425.

This means that Probability of rejecting null hypothesis when it is true is 0.425(Probability of committing type 1 error)