Question

A regression model to predict Y, the state-by-state 2005 burglary crime rate per 100,000 people, used the following four state predictors: X₁ = median age in 2005, X₂ = number of 2005 bankruptcies per 1,000 people, X₃ = 2004 federal expenditures per capita, and X₄ = 2005 high school graduation percentage.

Predictor	Coefficient
Intercept	4,286.0597
AgeMed	-26.986
Bankrupt	18.5775
FedSpend	-0.0280
HSGrad%	-28.5624

(a) Write the fitted regression equation. (Round your answers to 4 decimal places. Negative values should be indicated by a minus sign.)

yˆy^ =  +  AgeMed +  Bankrupt +  FedSpend +  HSGrad%

(b-1) The 2005 state-by-state crime rate per 100,000

	increases by about 27 as the state median age increases.
	decreases by about 27 as the state median age increases.

(b-2) The 2005 state-by-state crime rate per 100,000    

	decreases by about 19 for every 1,000 new bankruptcies filed.
	increases by about 19 for every 1,000 new bankruptcies filed.

(b-3) The 2005 state-by-state crime rate per 100,000           

	decreases by 0.028 for each dollar increase in federal funding per person.
	increases by 0.028 for each dollar increase in federal funding per person.

(b-4) The 2005 state-by-state crime rate per 100,000      

	decreases by about 29 for each 1% increase in high school graduations.
	increases by about 29 for each 1% increase in high school graduations.

(c) Would the intercept seem to have meaning in this regression?

	No
	Yes

(d) Make a prediction for Burglary when X₁= 34 years, X₂= 7.2 bankruptcies per 1,000, X₃= $5,044, and X₄= 84 percent.

Burglary Rate

rev: 09_26_2016_QC_CS-62964, 09_20_2017_QC_CS-1011

Answer 1

Y =The state-by-state 2005 burglary crime rate per 100,000 people.

X1 = median age in 2005

X2 = number of 2005 bankruptcies per 1,000 people

X3 = 2004 federal expenditures per capita

X4 = 2005 high school graduation percentage

a.

Predictor	Coefficient
Intercept	4,286.0597
AgeMed	-26.986
Bankrupt	18.5775
FedSpend	-0.0280
HSGrad%	-28.5624

The fitted regression equation

yˆ = 4,286.0597 -26.986 * AgeMed + 18.5775 *  Bankrupt - 0.0280 *FedSpend - 28.5624 *HSGrad%.

b.

The correct interpretation of the regression coefficients are :

(b-1) The 2005 state-by-state crime rate per 100,000 decreases by about 27 as the state median age increases

(b-2) The 2005 state-by-state crime rate per 100,000 increases by about 19 for every 1,000 new bankruptcies filed.

(b-3) The 2005 state-by-state crime rate per 100,000 decreases by 0.028 for each dollar increase in federal funding per person.

(b-4) The 2005 state-by-state crime rate per 100,000 decreases by about 29 for each 1% increase in high school graduations.

c.

No, there is no physical interpretation of the intercept in this problem except if all the regressors values become zero then the 2005 state-by-state crime rate per 100,000 is 4,286.0597 which makes no sense.

d.

We need to make a prediction for Burglary when X1 = 34 years, X2 = 7.2 bankruptcies per 1,000, X3 = $5,044, and X4 = 84 percent.

yˆ = 4,286.0597 -26.986 * 34 + 18.5775 *  7.2 - 0.0280 *5044 - 28.5624 *84 = 961 crime rate per 100,000