nsurance 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 perce
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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
Part 1 - SLR
The best SLR model for predicting Life Expectancy identifies murder rate as the most significant predictor.
1. Obtain and write the linear regression equation which uses murder rate only to predict life expectancy rate.
2. Comment on the R-square value in terms of how insurance companies might view these results in determining cost of coverage.
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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