Context:We are interested in understanding the family characteristics that determine the amount of insurance purchased by a household. We have access to the following information from a survey of households who have purchased term life insurance:FACE: The amount that the insurance company will pay in the event of the death of the named insured. This serves as a measure of the quantity of insurance owned by the household.INCOME: The total annual income of the household.EDUCATION: The number of years of education of the head of the household.NUMHH: The number of household members.MARSTAT: The marital status of the respondent of the survey. It takes values: 1 for married, 2 for living with partner, 0 for other.GENDER: Gender of the survey respondent. It takes value 1 if female and 0 otherwise.Please find attached the dataset TermLife.csv.Complete the following 2 questions:a) Perform the following coding tasks in R:Import the dataset TermLife.Look at the structure of the dataset using the function str() and look at the summary of the each variable using the function summary().Filter the dataset for values of FACE strictly positive.Encode MARSTAT as a factor variable using the function factor().Model A: Perform a multiple linear regression with FACE as the response and INCOME, EDUCATION, NUMHH, MARSTAT and GENDER as the predictors. Use the function summary() to print the results.Model B: Perform a multiple linear regression with log(FACE) as the response and log(INCOME), EDUCATION, NUMHH, MARSTAT and GENDER as the predictors. Use the function summary() to print the results.b) Comment on the results of fitting models A and B, justifying your responses. In particular, discuss: What predictors appear to have a statistically significant relationship to the response for each model? How well do the models fit the data?Compare models A and B. Which model fits the data better?Share any other findings you may find interesting.
Question
Context:We are interested in understanding the family characteristics that determine the amount of insurance purchased by a household. We have access to the following information from a survey of households who have purchased term life insurance:FACE: The amount that the insurance company will pay in the event of the death of the named insured. This serves as a measure of the quantity of insurance owned by the household.INCOME: The total annual income of the household.EDUCATION: The number of years of education of the head of the household.NUMHH: The number of household members.MARSTAT: The marital status of the respondent of the survey. It takes values: 1 for married, 2 for living with partner, 0 for other.GENDER: Gender of the survey respondent. It takes value 1 if female and 0 otherwise.Please find attached the dataset TermLife.csv.Complete the following 2 questions:a) Perform the following coding tasks in R:Import the dataset TermLife.Look at the structure of the dataset using the function str() and look at the summary of the each variable using the function summary().Filter the dataset for values of FACE strictly positive.Encode MARSTAT as a factor variable using the function factor().Model A: Perform a multiple linear regression with FACE as the response and INCOME, EDUCATION, NUMHH, MARSTAT and GENDER as the predictors. Use the function summary() to print the results.Model B: Perform a multiple linear regression with log(FACE) as the response and log(INCOME), EDUCATION, NUMHH, MARSTAT and GENDER as the predictors. Use the function summary() to print the results.b) Comment on the results of fitting models A and B, justifying your responses. In particular, discuss: What predictors appear to have a statistically significant relationship to the response for each model? How well do the models fit the data?Compare models A and B. Which model fits the data better?Share any other findings you may find interesting.
Solution
a) Here is how you can perform the tasks in R:
- Import the dataset TermLife:
TermLife <- read.csv("TermLife.csv")
- Look at the structure of the dataset and summary of each variable:
str(TermLife)
summary(TermLife)
- Filter the dataset for values of FACE strictly positive:
TermLife <- TermLife[TermLife$FACE > 0,]
- Encode MARSTAT as a factor variable:
TermLife$MARSTAT <- factor(TermLife$MARSTAT)
- Model A: Perform a multiple linear regression with FACE as the response and INCOME, EDUCATION, NUMHH, MARSTAT and GENDER as the predictors:
modelA <- lm(FACE ~ INCOME + EDUCATION + NUMHH + MARSTAT + GENDER, data = TermLife)
summary(modelA)
- Model B: Perform a multiple linear regression with log(FACE) as the response and log(INCOME), EDUCATION, NUMHH, MARSTAT and GENDER as the predictors:
modelB <- lm(log(FACE) ~ log(INCOME) + EDUCATION + NUMHH + MARSTAT + GENDER, data = TermLife)
summary(modelB)
b) To comment on the results of fitting models A and B, you would need to look at the p-values of the predictors in the summary output. Predictors with p-values less than 0.05 are considered to have a statistically significant relationship with the response.
The goodness of fit of the models can be assessed by looking at the R-squared value in the summary output. The closer the R-squared value is to 1, the better the model fits the data.
To compare models A and B, you can look at their respective R-squared values. The model with the higher R-squared value fits the data better.
Other interesting findings could include the direction and magnitude of the relationship between the predictors and the response, which can be inferred from the sign and value of the coefficients in the summary output.
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