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Question 1: state.X77 (25 points)

In # Explanatory modeling example 2 using R existing dataset called state.X77 from lab3, we conducted a set of analysis for the explanatory. Please leverage state.X77 to answer the following questions.

In Question 1, you do not need to split your data as training and validation sets.

1.1 Conduct correlation analysis on all variables and show which variable has the strongest positive and which variable has the strongest negative correlations with income. Show the correlations of the two variables. (Hints: be sure to rename some variables that have the space between two letters and also create a new variable called “Density” as we did in class). (2 points)

1.2 We are intended to model income as dependent variable. Based on your 1.1 answers, write down two hypotheses for each variable respectively (i.e., X influences Y, and what’s the effect direction?).

Ensure to provide reasons and arguments of why you have those hypotheses. (3 points)

1.3 Build a multiple linear regression model to examine your above two hypotheses where income is the dependent variable and the two variable are independent variables (called Model1). Show the summary of regression model. Explain the meaning of coefficients (significant or not? What’s the quantitative meaning of the coefficient?). Are the hypotheses supported? What’s the Adjusted R-Squared of the model?

Ensure to interpret your model results (5 points)

1.4 Build a second linear regression model for income, with Illiteracy, HSGrad and Density as IVs (called Model 2). Show the summary of regression model.

Are the coefficients very different from those in Model 1? What’s the Adjusted R-Squared of the model? Does this model fit the data better, compared to Model 1?

Ensure to interpret your model results (5 points)

1.5 Predict the following new data, using Model 2. Fill in the blanks. (5 points)

State Illiteracy HSGrad Density Income

State 1 1.0 48 100

State 2 0.7 50 70

State 3 2.0 45 440

State 4 1.4 47.5 15

1.6 Use (graphical) regression diagnostics and check the two assumptions for Model 2: non-linearity of residuals, normality of (distribution of) residuals. Are the two assumptions satisfied? Why? (5 points)

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