Question

A. Assume b0 = 12.953, and b1 = -2.5. For x = 25, predict y. Round to 3 digits.

B. if x is increased by 10 units, how much does y-hat change? Round to 3 digits.

Use the points to answer the following:

x	y
12	17
21	15
28	22
8	19
20	24

C. How much correlation is there between x and y? Round to four decimals and use leading zeros if necessary.

D. How much of the variability in y is explained by x? Round to four decimals and use leading zeros if necessary.

Answer 1

Part a)

Equation of linear regression is

We have b0 = 12.953, and b1 = -2.5. For x = 25, predict y.

Part b)

	X	Y	X * Y	X2
	12	17	204	144
	21	15	315	441
	28	22	616	784
	8	19	152	64
	20	24	480	400
Total	89	97	1767	1833

Equation of linear regression is

b = 0.1624

a = 16.5096

Equation becomes

When X = 10

Part c)

	X	Y	X * Y	X2	Y2
	12	17	204	144	289
	21	15	315	441	225
	28	22	616	784	484
	8	19	152	64	361
	20	24	480	400	576
Total	89	97	1767	1833	1935

Correlation coefficient is

Part d)

Coefficient of Determination

R² = r² = ( 0.3512 )² = 0.1233

12.33% of variability in y is explained by x.