Question

The teengamb dataset contains a survey that was conducted to study teenage gambling in Britain. The dataset has 47 observations and 5 variables: sex: 0= male, 1= female status: Socioeconomic status score based on parents' occupation income: income in pounds per week verbal: verbal score in words out of 12 correctly defined gamble: expenditure on gambling in pounds per year Use the following statement to access the data: data("teengamb", package = "faraway") Question 2.1: a. Create a new variable, male (1= male, 0= female). b. Fit a model with gamble as the response and the other variables (i.e., male, status, income, verbal, gamble) as predictors. c. Which variables are statistically significant at the 5% level? Question 2.2: Provide interpretation for the significant coefficients (of the model in Question 2.1c) Question 2.3: a. Use the confint function to produce 95% confidence intervals for the coefficients based on the same model. b. Can you deduce which coefficients are significant at the level of 5% based on the intervals? Question 2.4: Use the anova function to test the null hypothesis that the coefficients of sex and income are both 0 using the same model.

Answer 1

To analyze the teengamb dataset, a linear model is fitted with gambling expenditure as the response variable. Statistically significant predictors are identified based on p-values, and confidence intervals for coefficients are calculated. Interpretations and hypothesis tests further analyze the relationships in the data.Therefore, the correct option is C. X = 51, KL = 253, LM = 252.

Step-by-step explanation:

To address the student's question, a few steps have to be followed using statistical methods to analyze the teengamb dataset. First, let's tackle part 2.1 of the question:

1. Create a new variable called male where 1 corresponds to male and 0 to female. This is done by re-coding the existing sex variable. If the student is using R, this could be achieved with a command like teengamb$male <- ifelse(teengamb$sex == 0, 1, 0).
2. To fit a model with gamble as the response and the other variables as predictors, the lm() function can be used. The command could be model <- lm(gamble ~ male + status + income + verbal, data=teengamb).
3. To identify which variables are statistically significant at the 5% level, one would examine the summary of the model output, looking at the p-values (summary(model)$coefficients). Variables with p-values less than 0.05 are typically considered significant.

For parts 2.2, 2.3, and 2.4, the students would need to interpret the coefficients of the significant predictors, calculate the confidence intervals for the coefficients, and perform a hypothesis test on certain coefficients respectively.

Interpretation of the coefficients should reflect the direction and magnitude of the relationship between each predictor and the response variable.Therefore, the correct option is C. X = 51, KL = 253, LM = 252.