Insurance (Life Expectancy). Insurance companies base their premiums on many factors, but basically all the factors are variables that predict life expectancy. Life expectancy varies from place to place. The following variables are from a data set on various measures obtained from the 50 US states (around 2009) Murder: rate per 100,000 HS Graduation: recorded as a percentage Income: per capita income in dollars Illiteracy: rate per 1,000 Life Expectancy: recorded in years 2008 Electoral vote state color: red / blue State electoral vote color coded: red = 1 / blue = 0 Multiple linear regression results: See Attachments please Write the multiple linear regression equation, use this equation to predict the Life expectancy for Pennsylvania and calculate the residual. Data: State Name Life Expectancy Murder HS Grad Income Illiteracy ColorCode Color Alabama 69.05 15.1 41.3 3624 2.1 1 red Alaska 69.31 11.3 66.7 6315 1.5 1 red Arizona 70.55 7.8 58.1 4530 1.8 1 red Arkansas 70.66 10.1 39.9 3378 1.9 1 red California 71.71 10.3 62.6 5114 1.1 0 blue Colorado 72.06 6.8 63.9 4884 0.7 0 blue Connecticut 72.48 3.1 56 5348 1.1 0 blue Delaware 70.06 6.2 54.6 4809 0.9 0 blue Florida 70.66 10.7 52.6 4815 1.3 0 blue Georgia 68.54 13.9 40.6 4091 2 1 red Hawaii 73.6 6.2 61.9 4963 1.9 0 blue Idaho 71.87 5.3 59.5 4119 0.6 1 red Illinois 70.14 10.3 52.6 5107 0.9 0 blue Indiana 70.88 7.1 52.9 4458 0.7 1 red Iowa 72.56 2.3 59 4628 0.5 0 blue Kansas 72.58 4.5 59.9 4669 0.6 1 red Kentucky 70.1 10.6 38.5 3712 1.6 1 red Louisiana 68.76 13.2 42.2 3545 2.8 1 red Maine 70.39 2.7 54.7 3694 0.7 0 blue Maryland 70.22 8.5 52.3 5299 0.9 0 blue Massachusetts 71.83 3.3 58.5 4755 1.1 0 blue Michigan 70.63 11.1 52.8 4751 0.9 0 blue Minnesota 72.96 2.3 57.6 4675 0.6 0 blue Mississippi 68.09 12.5 41 3098 2.4 1 red Missouri 70.69 9.3 48.8 4254 0.8 1 red Montana 70.56 5 59.2 4347 0.6 1 red Nebraska 72.6 2.9 59.3 4508 0.6 1 red Nevada 69.03 11.5 65.2 5149 0.5 0 blue NewHampshire 71.23 3.3 57.6 4281 0.7 0 blue NewJersey 70.93 5.2 52.5 5237 1.1 0 blue NewMexico 70.32 9.7 55.2 3601 2.2 0 blue NewYork 70.55 10.9 52.7 4903 1.4 0 blue NorthCarolina 69.21 11.1 38.5 3875 1.8 1 red NorthDakota 72.78 1.4 50.3 5087 0.8 1 red Ohio 70.82 7.4 53.2 4561 0.8 0 blue Oklahoma 71.42 6.4 51.6 3983 1.1 1 red Oregon 72.13 4.2 60 4660 0.6 0 blue Pennsylvania 70.43 6.1 50.2 4449 1 0 blue RhodeIsland 71.9 2.4 46.4 4558 1.3 0 blue SouthCarolina 67.96 11.6 37.8 3635 2.3 1 red SouthDakota 72.08 1.7 53.3 4167 0.5 1 red Tennessee 70.11 11 41.8 3821 1.7 1 red Texas 70.9 12.2 47.4 4188 2.2 1 red Utah 72.9 4.5 67.3 4022 0.6 1 red Vermont 71.64 5.5 57.1 3907 0.6 0 blue Virginia 70.08 9.5 47.8 4701 1.4 0 blue Washington 71.72 4.3 63.5 4864 0.6 0 blue WestVirginia 69.48 6.7 41.6 3617 1.4 1 red Wisconsin 72.48 3 54.5 4468 0.7 0 blue Wyoming 70.29 6.9 62.9 4566 0.6 1 red

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Insurance (Life Expectancy).  Insurance companies base their premiums on many factors, but basically all the factors are variables that predict life expectancy.  Life expectancy varies from place to place.  The following variables are from a data set on various measures obtained from the 50 US states (around 2009)

Murder:  rate per 100,000

HS Graduation:  recorded as a percentage

Income:  per capita income in dollars

Illiteracy:  rate per 1,000

Life Expectancy: recorded in years

2008 Electoral vote state color:  red / blue

State electoral vote color coded:   red = 1 / blue = 0

Multiple linear regression results: See Attachments please

Write the multiple linear regression equation, use this equation to predict the Life expectancy for Pennsylvania and calculate the residual.

Data:

State Name Life Expectancy Murder HS Grad Income Illiteracy ColorCode Color
Alabama 69.05 15.1 41.3 3624 2.1 1 red
Alaska 69.31 11.3 66.7 6315 1.5 1 red
Arizona 70.55 7.8 58.1 4530 1.8 1 red
Arkansas 70.66 10.1 39.9 3378 1.9 1 red
California 71.71 10.3 62.6 5114 1.1 0 blue
Colorado 72.06 6.8 63.9 4884 0.7 0 blue
Connecticut 72.48 3.1 56 5348 1.1 0 blue
Delaware 70.06 6.2 54.6 4809 0.9 0 blue
Florida 70.66 10.7 52.6 4815 1.3 0 blue
Georgia 68.54 13.9 40.6 4091 2 1 red
Hawaii 73.6 6.2 61.9 4963 1.9 0 blue
Idaho 71.87 5.3 59.5 4119 0.6 1 red
Illinois 70.14 10.3 52.6 5107 0.9 0 blue
Indiana 70.88 7.1 52.9 4458 0.7 1 red
Iowa 72.56 2.3 59 4628 0.5 0 blue
Kansas 72.58 4.5 59.9 4669 0.6 1 red
Kentucky 70.1 10.6 38.5 3712 1.6 1 red
Louisiana 68.76 13.2 42.2 3545 2.8 1 red
Maine 70.39 2.7 54.7 3694 0.7 0 blue
Maryland 70.22 8.5 52.3 5299 0.9 0 blue
Massachusetts 71.83 3.3 58.5 4755 1.1 0 blue
Michigan 70.63 11.1 52.8 4751 0.9 0 blue
Minnesota 72.96 2.3 57.6 4675 0.6 0 blue
Mississippi 68.09 12.5 41 3098 2.4 1 red
Missouri 70.69 9.3 48.8 4254 0.8 1 red
Montana 70.56 5 59.2 4347 0.6 1 red
Nebraska 72.6 2.9 59.3 4508 0.6 1 red
Nevada 69.03 11.5 65.2 5149 0.5 0 blue
NewHampshire 71.23 3.3 57.6 4281 0.7 0 blue
NewJersey 70.93 5.2 52.5 5237 1.1 0 blue
NewMexico 70.32 9.7 55.2 3601 2.2 0 blue
NewYork 70.55 10.9 52.7 4903 1.4 0 blue
NorthCarolina 69.21 11.1 38.5 3875 1.8 1 red
NorthDakota 72.78 1.4 50.3 5087 0.8 1 red
Ohio 70.82 7.4 53.2 4561 0.8 0 blue
Oklahoma 71.42 6.4 51.6 3983 1.1 1 red
Oregon 72.13 4.2 60 4660 0.6 0 blue
Pennsylvania 70.43 6.1 50.2 4449 1 0 blue
RhodeIsland 71.9 2.4 46.4 4558 1.3 0 blue
SouthCarolina 67.96 11.6 37.8 3635 2.3 1 red
SouthDakota 72.08 1.7 53.3 4167 0.5 1 red
Tennessee 70.11 11 41.8 3821 1.7 1 red
Texas 70.9 12.2 47.4 4188 2.2 1 red
Utah 72.9 4.5 67.3 4022 0.6 1 red
Vermont 71.64 5.5 57.1 3907 0.6 0 blue
Virginia 70.08 9.5 47.8 4701 1.4 0 blue
Washington 71.72 4.3 63.5 4864 0.6 0 blue
WestVirginia 69.48 6.7 41.6 3617 1.4 1 red
Wisconsin 72.48 3 54.5 4468 0.7 0 blue
Wyoming 70.29 6.9 62.9 4566 0.6 1 red
Multiple linear regression results without using State color:
Stepwise results:
P-value to enter: 0.15
P-value to leave: 0.25
Variable
Murder
HS Grad
Step
P-value
R-squared
R-squared (adj)
Action
RMSE
Entered
Entered
1
<0.0001
0.8473
0.6097
0.6016
2
0.0091
0.7959
0.6628
0.6485
Parameter estimates:
Parameter
Estimate
Std. Err.
Alternative
DF
T-Stat
P-Value
Intercept
70.297
1.016
47
69.212668
<0.0001
Murder
-0.237
0.035
47
-6.7192441
<0.0001
HS Grad
0.044
0.016
47
2.7213744
0.0091
Summary of fit:
Root MSE: 0.7959
R-squared: 0.6628
R-squared (adjusted): 0.6485
Transcribed Image Text:Multiple linear regression results without using State color: Stepwise results: P-value to enter: 0.15 P-value to leave: 0.25 Variable Murder HS Grad Step P-value R-squared R-squared (adj) Action RMSE Entered Entered 1 <0.0001 0.8473 0.6097 0.6016 2 0.0091 0.7959 0.6628 0.6485 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-Value Intercept 70.297 1.016 47 69.212668 <0.0001 Murder -0.237 0.035 47 -6.7192441 <0.0001 HS Grad 0.044 0.016 47 2.7213744 0.0091 Summary of fit: Root MSE: 0.7959 R-squared: 0.6628 R-squared (adjusted): 0.6485
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