Question

36, Max believes that the sales of coffee at his coffee shop depend upon the weather. He has taken a sample of 5 days. Below you are given the results of the sample. Cups of Coffee Sold 350 200 Temperature 50 60 210 100 70 80 60 90 40 100 Which variable is the dependent variable? a. of Coffee sold Cups b. Compute the least squares estimated line. Compute the correlation coefficient between temperature and the sales of coffee. c. d. Is there a significant relationship between the sales of coffee and temperature? Use a .05 level of significance and t--6.218. Be sure to state the null and alternative hypotheses. Predict sales of a 90 degree day. e. 37. The following sample data contains the number of years of college and the current annual salary for a random sample of heavy equipment salespeople. Years of College Annual Income (In Thousands) 2 20 2 23 25 3 4 26 3 29 27 30 33 35 RAaa8an8as 454 t

Answer 1

36)

a) Dependent variable = Coffee cups sold

b) Let Equation be y= a+bx

Sl. No.	Temperature (x)	Coffee sold (y)	x^2	y^2	x*y
1	50	350	2500.00	122500.0	17500
2	60	200	3600.00	40000.0	12000
3	70	210	4900.00	44100.0	14700
4	80	100	6400.00	10000.0	8000
5	90	60	8100.00	3600.0	5400
6	100	40	10000.00	1600.0	4000
Total	450	960	35500	221800	61600
Average	75.000	160

(1η : ) (α 1: )- α 7- 1ης (νη . 3) - 47-4ς

Sxx	1750
Syy	68200
Sxy	-10400

b = Sxy/Sxx = -10400/1750 = -5.943

a = = 160 - (-5.943*75) = 605.71

4 - 03

y = 605.71 - 5.943x

c) Correlation coefficient = r = = -0.952

Sry Sur * Syy

d) critical value = = t_0.025,4 = 2.776

ta/2,1-2

since | t | is greater than critical value we reject null hypothesis and there is a significant evidence to conclude that slope is not equal to zero.

e) sales for 90 degree day => y = 605.71 - 5.943*90 = 70.84 which is approximately 71.

37)

a) y = a + bx

dependent variable = Annual Income, Independent variable = Years of college.

b)

Sl. No.	years of college	Annual Income	x^2	y^2	x*y
1	2	20	4.00	400.0	40
2	2	23	4.00	529.0	46
3	3	25	9.00	625.0	75
4	4	26	16.00	676.0	104
5	3	28	9.00	784.0	84
6	1	29	1.00	841.0	29
7	4	27	16.00	729.0	108
8	3	30	9.00	900.0	90
9	4	33	16.00	1089.0	132
10	4	35	16.00	1225.0	140
Total	30	276	100	7798	848
Average	3	27.6

Sxx	10
Syy	180.4
Sxy	20

y = 21.6 + 2x

c) for x = 1

y = 21.6 + 2 = 23.6

d) ANOVA table

ANOVA
	df	SS	MS	F	Significance F
Regression	1	b*Sxy = 40	40	2.279202	0.169559
Residual	8	Syy - b*Sxy = 140.4	MSE = 17.55
Total	9	Syy = 180.4

t = = 1.510

MSE/Sex

critical value = t_0.025,8 = 2.306

since | t | is less than critical value we fail to reject null hypothesis and there is a no significant evidence to conclude that slope is not equal to zero. there is no linear relation associated between the variables.

e) R² = SS_Regression/ SS_Residual = 0.2217

f) correlation coefficient = sqrt(R²) = 0.4708 ( positive because slope is positive)

The variables have weaker positive correlation.

38) R² is always smaller than correlation coefficient.

39) error term is assumed to be normally distributed.