Question

1.) Sketch a scatter plot from the following data, and determine the equation of the regression line. x 125 119 103 91 50 29 24 y

2.)Investment analysts generally believe the interest rate on bonds is inversely related to the prime interest rate for loans; that is, bonds perform well when lending rates are down and perform poorly when interest rates are up. Can the bond rate be predicted by the prime interest rate? Use the following data to construct a least squares regression line to predict bond rates by the prime interest rate. Bond Rate 5% 11 9 16 7 Prime Interest Rate 17% 6 8 5 7

3.)The equation of a regression line is = 51.393 – 1.701 and the data are as follows. x 5 8 11 12 18 25 y 46 38 32 26 22 10 a. Solve for the residuals. b.Graph a residual plot. c.Do these data seem to violate any of the assumptions of regression?

Answer 1

Solution:

3.(a)

The scatter plot of the data is:

The fitted regression equation of Y on X is:

The value of the residuals are given in the following table:

x	y	Predicted	Residual
5	46	42.89	3.11
8	38	37.79	0.21
11	32	32.69	-0.69
12	26	30.99	-4.99
18	22	20.79	1.21
25	10	8.89	1.11

(b).

The residual plot is given below:

(c). From the residual plot,we observe there is no clear pattern in the plot and the plot is quite random. Hence, the regression is perfect. The data does not seem to violet any of the assumptions of the regression.