3. US State Demographics (circa 2000?)

Here is a dataset on various measures of the 50 States plus DC. The variables include:

Violent Crimes: rate per 100,000

Median Household Income: dollars

Mean Personal Income: dollars

Population: Total population in the state

M.D.s: rate per 100,000

3a. Why might researchers consider both Median Household Income and Mean Personal income? (3pts)

The mean is helpful in understanding if the data is symmetrical. However, the mean accounts for outliers within the data. Therefore the median is important because it neglects the effect of outliers to avoid errors.

3b. Perform the appropriate two-sample t-test to determine if mean violent crime rate per 100,000 population is significantly different between the Red and Blue states. (Copy and paste necessary output to confirm your findings.) Clearly state the conclusion of your test in terms of the research question.

(6 pt)

Interpreting the correlation matrix:

The goal of the present research is to find the best linear model for predicting Violent Crimes

Use the correlation matrix below to answer 3c-3e below:

3c. Which factor appears to be the single strongest predictor of violent crimes and why? (3 pts)

3d. Which factor appears to be the least significant predictor of violent crimes and why? (3 pts)

3e. Which independent predictor variables show signs of multi-collinearity with each other? And discuss these relationships. (6 pts)

The following provides the output from all the potential significant two-variable and three variable linear models.

3f. Why did I choose M.D.s to be in all of these two-variable models? (3 pts)

3g. Write the estimated linear regression model which is the best two-variable MLR model and explain why you chose this model. (6 pts)

The following output selected some 3 variable MLR models that showed promise.

3h. Economic research often relaxes the significant level to = 0.10. Do any of the models provided in the above output yield a usable 3-variable model for predicting violent crimes given state demographic measures? Explain. (5 pts)

The following output was provided by the stepwise linear regression option in StatCrunch.

Statcrunch provided the following MLR model as the best economic model to use when predicting violent crimes:

Predicted Violent crimes per 100,000 = -350.31 + 1.91 M.D._s per 100,000 + 29.54 Percent poverty + 0.000009833 Population

3i. Given the steps provided from Excel modeling, do you agree with Statcrunchs results? Explain.

(4 pts)

3j. Interpret the slope coefficient for Percent poverty in the context of predicting violent crimes. (4 pts)

3k. The slope coefficient for Population is so tiny, 0.000009833. Using a significance level of 0.10, explain how a coefficient that is so close to zero could turn out to be a significant slope. (4 pts)