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 4,579.5465
AgeMed -27.292 Bankrupt 19.5612
FedSpend -0.0264
HSGrad% -27.5839

(a) Write the fitted regression equation. (Round your answers to 4 decimal places. Negative values should be indicated by a minus sign.)
yˆ = ____+____ AgeMed +____ Bankrupt + ____FedSpend + ____HSGrad%

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

(b-2) The 2005 state-by-state crime rate per 100,000
increases by about 20 for every 1,000 new bankruptcies filed
decreases by about 20 for every 1,000 new bankruptcies filed.

(b-3) The 2005 state-by-state crime rate per 100,000
decreases by 0.0264 for each dollar increase in federal funding per person
increases by 0.0264 for each dollar increase in federal funding per person.

(b-4) The 2005 state-by-state crime rate per 100,000
increases by about 28 for each 1% increase in high school graduations
decreases by about 28 for each 1% increase in high school graduations.

c) Would the intercept seem to have meaning in this regression?
Yes
No

(d) Make a prediction for Burglary when X1 = 35 years, X2 = 5.7 bankruptcies per 1,000, X3 = $5,864, and X4 = 84 percent.
Burglary Rate=

Answer 1

a)

yˆ = 4,579.5465-27.292* AgeMed +19.5612*Bankrupt -0.0264*FedSpend -27.5839*HSGrad%

b1)

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

b2)

The 2005 state-by-state crime rate per 100,000
increases by about 20 for every 1,000 new bankruptcies filed

b3)

The 2005 state-by-state crime rate per 100,000
decreases by 0.0264 for each dollar increase in federal funding per person

b4)

The 2005 state-by-state crime rate per 100,000
decreases by about 28 for each 1% increase in high school graduations

c)

Yes, intercept is the mean value of yˆ when Independent variables are equal to 0

d)

yˆ = 4,579.5465-27.292* AgeMed +19.5612*Bankrupt -0.0264*FedSpend -27.5839*HSGrad%

X1 = 35 years, X2 = 5.7 bankruptcies per 1,000, X3 = $5,864, and X4 = 84 percent

yˆ = 4,579.5465-27.292* 35 +19.5612*5.7 -0.0264*5864 -27.5839*84

Burglary Rate = yˆ = 1263.968

If X4 = 84 percent = 0.84

Burglary Rate = yˆ = 3557.845