Question

Jason believes that the sales of coffee at his coffee shop depend upon the weather. He has taken a sample of 6 days varying in degrees of temperature. Below you are given the results of the sample.

Cups of Coffee Sold	Temperature (in ⁰F)
350	50
200	60
220	70
110	80
65	90
40	100

​

a. In this scenario, the dependent variable is .

b. The least squares estimated regression equation is .

c. The correlation coefficient (to four decimal places) between temperature and the sales of coffee is  .

d. The predicted sales of a 90-degree day is .

e. The residual for sales on a 90-degree is .

Answer 1

	Temperature X	Cup of coffee Y	X * Y
	50	350	17500	2500	122500
	60	200	12000	3600	40000
	70	220	15400	4900	48400
	80	110	8800	6400	12100
	90	65	5850	8100	4225
	100	40	4000	10000	1600
Total	450	985	63550	35500	228825

Part a)

Dependent variable is cup of coffee sold

Part b)

Equation of regression line is


b = -5.9

a =( 985 - ( -5.9 * 450 ) ) / 6
a = 606.667
Equation of regression line becomes

Part c)

r = -0.9527

Part d)

When X = 90
= 606.667 + -5.9 X
= 606.667 + -5.9 * 90
= 75.67

Part e)

Residual = Y -

Residual = 65 - 75.67

Residual = -10.67