Question

y, Crime Rate (Number of Crimes per 1,000 in population)

x1, Total Population (in thousands)

x2, Percent of Students Receiving Free Lunch

ANOVA
	df	SS	MS	F-Statistic	p-value
Regression	2	55,423	27,712	25.923	<0.0001
Residual	42	44,909	1,069
Total	44	100,332
	Coefficients	Standard Error	t-Statistic	p-value
Intercept	68.398	16.492	4.147	0.0002
Total Population	-4.743	1.660	-2.857	0.0066
Percent Free Lunch	1.215	0.224	5.424	<0.0001

a) By how much does the model estimate the crime rate would change due to a 1% increase in the percentage of students receiving free lunch (assuming all other things are constant)? What about 2.5%?

b) By how much does the model estimate the crime rate would decrease due to a 1,000 person increase in the total population (assuming all other things are constant)?

c) By how much does the model estimate the crime rate would change due to a 5,000 person increase in the total population (assuming all other things are constant)?

d) Use the full model specified above to predict the crime rate for a Denver neighborhood with a total population of 7,000 and 18% of the student population receiving free lunch. (Enter your answer to three decimal places.)

Answer 1

(A) Slope of percent free lunch is 1.215, positive value indicating that it will increase the crime rate.

So, crime rate would increase by 1.215 due to a 1% increase in the percentage of students receiving free lunch

For 2.5%, crime rate increase by 2.5*1.215 = 3.0375

(B) Slope of total population is -4.743, negative value indicating that it will decrease the crime rate

So,  crime rate would decrease by 4.743 due to a 1,000 person increase in the total population

(C) Slope of total population is -4.743, negative value indicating that it will decrease the crime rate

and we know that crime rate would decrease by 4.743 due to a 1,000 person increase in the total population

so, decrease due to 5000 people = 5*(4.743) = 23.715 (decrease)

crime rate would decrease by 23.715 due to a 5,000 person increase in the total population

(D) Regression equation is

crime rate = 68.398 - 4.743(population) + 1.215(percent free lunch)

setting population= 7 (thousand) and percent free lunch = 18

we get

crime rate = 68.398 - 4.743(7) + 1.215(18)

= 57.067