In this problem, we will analyze the effect of categorized PROP_LUNCH on the variable CRIME_RATE when accounting for PROP_CHANGE_INCOME. The researchers decided to categorize the variable PROP_LUNCH into 3 categories: Lunch A = “Neighborhoods with no more than 33% of schools participating in free school lunch program” Lunch B = Neighborhoods more than 33% but no more than 66% of schools participating in free school lunch program” Lunch C = “Neighborhoods more than 66% of schools participating in free school lunch program” Give the estimated model :crime_rate = 142.5737 - 1.9215(Prop_change_income) -38.8741(Lunch A) - 19.20521(Lunch B)
In this problem, we will analyze the effect of categorized PROP_LUNCH on the variable CRIME_RATE when accounting for PROP_CHANGE_INCOME. The researchers decided to categorize the variable PROP_LUNCH into 3 categories:
Lunch A = “Neighborhoods with no more than 33% of schools participating in free school lunch program”
Lunch B = Neighborhoods more than 33% but no more than 66% of schools participating in free school lunch program”
Lunch C = “Neighborhoods more than 66% of schools participating in free school lunch program”
Give the estimated model :crime_rate = 142.5737 - 1.9215(Prop_change_income) -38.8741(Lunch A) - 19.20521(Lunch B)
(1) For neighborhoods with more than 66% of schools participating in free school lunch program, the estimated regression model is:crime_rate = 142.5737 - 1.9215(Prop_change_income) - 38.8741(0) - 19.20521(0) = 142.5737 - 1.9215(Prop_change_income)
(2) For neighborhoods with 33% to 66% of schools participating in free school lunch program, the estimated regression model is:crime_rate = 142.5737 - 1.9215(Prop_change_income) - 38.8741(0) - 19.20521(1) = 123.36849 - 1.9215(Prop_change_income)
(3) For neighborhoods with less than 33% of schools participating in free school lunch program, the estimated regression model is:crime_rate = 142.5737 - 1.9215(Prop_change_income) - 38.8741(1) - 19.20521(0) = 103.69959 - 1.9215(Prop_change_income)
Question:Test whether the crime rate in neighborhoods with 33% to 66% of schools participating in free school lunch program is significantly different than the crime rate in neighborhoods with more than 66% of schools participating in free school lunch program when adjusting for percent change in household income over past several years using a partial F test. Don't forget to specify the null and alternative hypothesis, test statistic, degrees of freedom, p-value, decision and conclusion in the words of the problem. Use level of significance 5%.
![Source
Model
Error
DF
3
37
Corrected Total 40
Variable
Intercept
Analysis of Variance
Sum of
Squares
11441
35693
47134
Root MSE
Dependent Mean
Coeff Var
Mean
Square
3813.66026
964.67401
Parameter Estimates
DF
F Value
3.95
31.05920 R-Square 0.2427
73.79512 Adj R-Sq 0.1813
42.08842
Parameter Standard
Estimate
1 142.57372
25.11823
prop_change_income
0.86875
1 -1.92158
prop_lunch_cat_LunchA 1 -32.87418 12.68270
prop_lunch_cat_LunchB 1 -19.20521 11.74957
Pr > F
0.0153
Error t Value
Pr> t
5.68
<.0001
-2.21
0.0332
-2.59
0.0136
-1.63 0.1106](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff0b45d0-95e9-4516-aa8d-2049cab09c1c%2F79cf5319-181d-4529-b6e8-9da4e53dbe2a%2F9phkkt_processed.png&w=3840&q=75)
![Analysis of Variance
Sum of
Squares
1 4880.98991
39
Corrected Total 40
Source
Model
Error
DF
Variable
Intercept
42253
47134
Mean
Square
4880.98991
1083.40844
Root MSE
32.91517 R-Square 0.1036
Dependent Mean 73.79512 Adj R-Sq 0.0806
Coeff Var
44.60345
Parameter Estimates
DF
1
prop_change_income 1 -1.94182
Parameter Standard
Estimate
125.52814 24.90924
0.91485
F Value
4.51
Pr > F
0.0402
Error t Value Pr> |t|
5.04 <.0001
-2.12 0.0402](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff0b45d0-95e9-4516-aa8d-2049cab09c1c%2F79cf5319-181d-4529-b6e8-9da4e53dbe2a%2Fs3rfmzm_processed.png&w=3840&q=75)
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