Question

Q1 In a laboratory experiment, data were gathered on the life span (Y in months) of 33 rats, units of daily protein intake (X1), and whether or not a proposed life extending agent was added to the rats diet (X2 = 0 if agent was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed: y bar = 10 - 18x1 + 3X2 = 14X3 Also provided are SSR = 60 and SST = 180. Refer to Exhibit 16-4.
a) The p-value for testing the significance of the regression model is

b) The life expectancy of a rat that was given 2 units of the proposed life extending agent daily but was not given any protein is:

c) The degrees of freedom associated with SSE are

d) The life expectancy of a rat that was not given any protein and that did not take the proposed life extending agent

Q2 A variable Z, whose value is Z = X₁X₂, is added to a general linear model in order to account for potential effects of the two variables X₁ and X₂ acting together. This type of effect is:

Select one:

a. Impossible to occur

b. Called interaction

c. Called multicollinearity effect

d. Called transformation effect

Q3 When dealing with the problem of non-constant variance, the reciprocal transformation means using:

Select one:

a. 1/X as the independent variable instead of X

b. X² as the independent variable instead of X

c. Y² as the dependent variable instead of Y

d. 1/Y as the dependent variable instead of Y

Answer 1

Q1 In a laboratory experiment, data were gathered on the life span (Y in months) of 33 rats, units of daily protein intake (X1), and whether or not a proposed life extending agent was added to the rats diet (X2 = 0 if agent was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed: y bar = 10 - 18x1 + 3X2 Also provided are SSR = 60 and SST = 180. Refer to Exhibit 16-4.
a) The p-value for testing the significance of the regression model is

P=0.002

b) The life expectancy of a rat that was given 2 units of the proposed life extending agent daily but was not given any protein is:

y =10-18*0+3*1 = 13

c) The degrees of freedom associated with SSE are 30

(N-k-1= 33-2-1=30)

d) The life expectancy of a rat that was not given any protein and that did not take the proposed life extending agent

y =10-18*0+3*0 = 10

Q2 A variable Z, whose value is Z = X₁X₂, is added to a general linear model in order to account for potential effects of the two variables X₁ and X₂ acting together. This type of effect is:

Select one:

a. Impossible to occur

Answer: b. Called interaction

c. Called multicollinearity effect

d. Called transformation effect

Q3 When dealing with the problem of non-constant variance, the reciprocal transformation means using:

Select one:

Answer: a. 1/X as the independent variable instead of X

b. X² as the independent variable instead of X

c. Y² as the dependent variable instead of Y

d. 1/Y as the dependent variable instead of Y