Question

For the data x= 1,4,5 , and y= 2, 7, 11

1. a.) Find the correlation coefficient r? What type of relationship does this represent? Explain. Show all work and calculations for credit. The formula will be provided on the board.
2. b.) Now find our r squared= coefficient of determination. What does this number tell you in regards to our explanatory variable x and how it explains our response variable y?
3. c.) Let’s say if our regression equation is. Y= 2.1154x – 0.3846, Let’s say x= speed of car and y= stopping distance in feet. if we another variable x2 = speed of wind to the regression equation and our new regression equation is Y= 3.2x + 2.1x2+ 4.2 , would the speed of the wind be a confounding or lurking variable (hint: Go by the 15% change in rule).

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
1	2	5.44	21.78	10.89
4	7	0.44	0.11	0.22
5	11	2.78	18.78	7.22

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	10	20	8.666666667	40.7	18.33
mean	3.33	6.67	SSxx	SSyy	SSxy

A)

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.9766
IT REPRESENTS A LINEAR STRONG RELATIONSHIP BETWEEN X AND Y

.......

B)

coefficient of determination, R² =    (Sxy)²/(Sx.Sy) =    0.9537

R² = 95.37% . it implies that 95.37% values are explained by our explainatry variable x to the response of Y

.........

C)

Y= 3.2x + 2.1x2+ 4.2

x2 is confounding variable

thanks

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