I'll load the data and analyze it to select two independent variables that may work well for a multiple linear regression. Then I'll outline steps to perform a full regression analysis in R and Minitab, including assumption testing, model fit, and interpretations.

Let’s start by examining the structure of the dataset and looking at potential variables.The dataset includes multiple variables. Key numeric variables we could use for a multiple linear regression model include:

1. Life Expectancy (dependent variable)
2. Adult Mortality
3. GDP
4. Schooling
5. Alcohol Consumption

We'll proceed with Adult Mortality and Schooling as independent variables, given their likely impact on life expectancy based on health and education levels.

Here's a general outline to perform the analysis in R and Minitab.

Step 1: Model Regression

• Use lm() in R to create a multiple linear regression model:

  RCopy code
  model <- lm(`Life expectancy ` ~ `Adult Mortality` + Schooling, data = dataset)
  summary(model)

• In Minitab, import the dataset, choose Stat > Regression > Regression > Fit Regression Model, set Life expectancy as the response, and add Adult Mortality and Schooling as predictors.

Step 2: Assumption Testing

• Normality of Residuals: Use a Q-Q plot or Shapiro-Wilk test (shapiro.test(residuals(model)) in R).
• Linearity: Check scatter plots of predictors vs. residuals.
• Homoscedasticity: In R, use plot(model, which = 3).
• Multicollinearity: Calculate Variance Inflation Factor (VIF) with car::vif(model).

Step 3: F-test (Overall Significance Test)

• R’s model summary includes the F-statistic to test overall significance.

Step 4: Partial T-tests (Significance of Each Variable)

• In R, the summary(model) command shows individual t-tests for each predictor. In Minitab, these are listed as p-values in the model output.

Step 5: Coefficient of Determination (R²)

• Found in the model summary under Multiple R-squared in R, indicating the proportion of life expectancy variance explained by the model.

Let me know if you need further guidance or have specific questions on any steps.

Follow-up Questions

1. How are the regression assumptions verified in practical datasets?
2. What specific conditions make multicollinearity problematic?
3. How can we interpret the coefficients in a regression output?
4. What do we conclude if the overall F-test is not significant?
5. How do we handle missing data before running a regression?

Tip: Always check multicollinearity (VIF) to ensure predictors do not overly influence each other, ensuring the stability of your regression model.