Question

and y Given are five observations for two variables, 7 20 17 13 29 13 48 52 58 a. Choose the correct scatter diagram for these data: B. 60- 60 50- 50 40 30- 30 20- 20 10- 10 40 60 x 50 30 60 v 20 10 4C 50 30 10 D C y y 60- 60 50- 50 40- 40 30- 30 60+ 60+ 50- 50- 40+ 40- 30+ 30- 20+ 20+ 10+ 10 10 20 30 40 50 10 20 30 40 50 60 x Select your answer b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? linear relationship between There appears to a Select your answer and y c. Try to approximate the relationship between and by drawing a straight line through the data. to provide a linear approximation of the relationship between and y. Select your answer d. Develop the estimated regression equation by computing the values of bo and b using equations: (Enter negative values as negative figure) (-)( ) (-) (to decimals) = 4. e. Use the estimated regression equation to predict the value of y when (to 2 decimals)

Answer 1

a) Scatter plot: Answer A

A. 60 50 40 30 10- 30 10 40 50 60 20

b) there appears to be a Negative linear relationship between x and y.

c) A straight line to provide a linear approximation of the relationship between x and y.

d)

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
3	58	81	324	-162
13	48	1	64	8
7	52	25	144	-60
20	13	64	729	-216
17	29	25	121	-55
ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
60	200	196	1382	-485

x̅ = Ʃx/n = 12

y̅ = Ʃy/n = 40

485 Slope, b i-)(yi- -2.474490 Σ(- 196 Intercept, bo b1 40-(-2.474490) 12 69.693878

Regression equation :

ŷ = 69.69 + (-2.47)x

e) Predicted value of y at X = 4

ŷ = 69.6939 + (-2.4745) * 4 = 59.80