Question

Assume that the sales of coffee at his coffee shop depend upon the weather. He has taken a sample of 6 days. Below you are given the results of the sample.

Cups of Coffee Sold	Temperature
340	50
200	60
210	70
100	80
60	90
40	100

a.	Which variable is the dependent variable?
b.	Using the Excel spreadsheet, run the least squares model and write the summary output here.
c.	Compute the least squares estimated line.
d.	Compute the correlation coefficient between temperature and the sales of coffee.
e.	Is there a significant relationship between the sales of coffee and temperature? Use a .05 level of significance. Be sure to state the null and alternative hypotheses.
f.	Predict sales of a 90 degree day.

Answer 1

a)

dependent variable : Cups of Coffee Sold

b)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9555
R Square	0.9129
Adjusted R Square	0.8912
Standard Error	37.4611
Observations	6.0000
ANOVA
	df	SS	MS	F	Significance F
Regression	1	58870	58870	41.9501	0.0029
Residual	4	5613.333333	1403.333333
Total	5	64483.33333
	Coefficients	Standard Error	t Stat	P-value
Intercept	593.3333	68.8811	8.6139	0.0010
Temperature	-5.8000	0.8955	-6.4769	0.0029

c) e least squares estimated line. :Yhat=593.3333-5.8000*temperature

d)

correlation coefficient =-0.9555

e)

null hypothesis:		β1	=	0
Alternate Hypothesis:		β1	≠	0

as p value =0.0029 is less than 0.05 ; we reject null hypothesis and conclude that there is a significant relationship between the sales of coffee and temperature .

f)

predicted sales =593.3333-5.8000*90=71.3333