g. Using the model in part a., the predicted robbery rate for a southern state i

Question

g. Using the model in part a., the predicted robbery rate for a southern state is 85.375 robberys reported to the police per 100,000 population h. What percentage of the total variability in robbery rates is "explained" by knowing whether a state is southern and how many males there are per 1000 females in that state? i. What percentage of the total variability in robbery rates is "explained" by knowing whether a state is southern, how many males there are per 1000 females in that state, and the 1960 expenditure on police by state and local government? j. Consider the model in part c., which uses "Southern" and "Expend1960" as predictors. Use this model to predict the following Robbery rate for a southern state that had $4400 per capita expenditure on police by state and local government: Robbery rate for a non-southern state that had $5500 per capita expenditure on police by state and local government: k Construct approximate 95% confidence intervals for the estimated slope coefficients b1 and b2) in this model (part c ), using the usual approximate value t- critical-2 Slope coefficient for Southern Margin of error CI lower bound Slope coefficient for Expend1960: Margin of error CI lower bound CI upper bound CI upper bound

Explanation / Answer

Here dependent variable is robbery rate and independent variables are southern, expend1960 and males per female.

Now we have given four different models with different independent variables.

We can do regression in EXCEL.

steps :

ENTER data into excel sheet --> Data --> Data analysis --> Regression --> ok --> Input Y range : select dependent variable --> Input X range : select independent variables --> Labels --> Output range : select one empty cell --> ok

So the four models are :

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0.64907

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For all the answers we use these outputs.

h) The percentage of total variability in robbery rates is explained by knowing whether a state is southern and how many males there are per 1000 females in the state is 4.84%.

i) The percentage of total variability in robbery rates is explained by knowing whether a state is southern and how many males there are per 1000 females and the 1960 expenditure on police by state and local government is 57.49%.

j) Now we have to predict robbery rate for expend1960 = $4400 and southern = 1

Here we use regression equation to find robbery rate.

The regression equation is,

Robbery rate = 1.32 + 15.15*southern + 0.99*expend1960

= 1.32 + 15.15*1 + 0.99*4400

= 4363.03

Now again we have to find robbery rate for southern = 0 and expend1960 = $5500

Robbery rate = 1.32 + 15.15*0 + 0.99*5500

= 5434.53

K) Construct 95% confidence interval for slope.

95% confidence interval for southern is (-3.49, 33.79)

95% confidence interval for expend1960 is (0.69, 1.29)

SUMMARY OUTPUT Regression Statistics Multiple R 0.095152 R Square 0.009054 Adjusted R Square -0.01297 Standard Error 38.97372 Observations 47 ANOVA df SS MS F Significance F Regression 1 624.5197 624.5197 0.411152 0.524638 Residual 45 68352.8 1518.951 Total 46 68977.32 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 93.06774 6.999887 13.29561 3.42E-17 78.96925 107.1662 78.96925 107.1662 southern -7.69274 11.9972 -0.64121 0.524638 -31.8563 16.47086 -31.8563 16.47086

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