Question

can i get help plz asap

4. A consumer welfare agency wants to investigate the relationship between the sizes of houses and the rents paid by tenants. The agency collected the following data on the sizes (in hundreds of square feet) of six houses and the monthly rents (in dollars) paid by tenants. Size of home 2315 22 2835 22 Monthly rent 1050 850 1000 1250 1550 1100 a. Find and state the equation of the regression line y = ax +b with size of house as an independent variable and monthly rent as a dependent variable. b. Predict the monthly rent for a house with 2600 square feet. c. Give the coefficient of correlation, r. d. Sketch the scatter plot and regression line in the box below.

Answer 1

X	Y	XY	X²	Y²
23	1050	24150	529	1102500
15	850	12750	225	722500
22	1000	22000	484	1000000
28	1250	35000	784	1562500
35	1550	54250	1225	2402500
22	1100	24200	484	1210000
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
145	6800	172350	3731	8000000

Sample size, n =	6
x̅ = Ʃx/n = 145/6 =	24.1666667
y̅ = Ʃy/n = 6800/6 =	1133.33333
SSxx = Ʃx² - (Ʃx)²/n = 3731 - (145)²/6 =	226.833333
SSyy = Ʃy² - (Ʃy)²/n = 8000000 - (6800)²/6 =	293333.333
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 172350 - (145)(6800)/6 =	8016.66667

a)

Slope, a = SSxy/SSxx = 8016.66667/226.83333 = 35.341661

y-intercept, b = y̅ - a* x̅ = 1133.33333 - (35.34166)*24.16667 = 279.2432

Regression equation :

ŷ = 35.3417 x + 279.2432

b)

Predicted value of y at x = 26

ŷ = (35.3417) * 26 + 279.2432 = 1198.1264

c) Correlation coefficient, r = SSxy/√(SSxx*SSyy)

= 8016.66667/√(226.83333*293333.33333) = 0.9828

d) Plot:

Scatterplot 1800 1600 1400 Monthly rent 10 30 40 20 Size of home

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