will be preferred.
1. [Crime rate] A criminologist studying the relationship between level of education and crime rate in medium-sized U.S counties collected the attached data for a random sample of 84 counties. Here X is the percentage of individuals in the county having at least a high-school diploma and Y is the crime rate (crime per 100,000 residents).
1. [2+2+2=6] Create a scatterplot of the above data and comment on the perceived relationship between education and crime rate. Quantify the strength of linearity using a relevant measure.
2. [2] Regress average crime rate on education and write down the estimated least squares re- gression model.
3. [2] Communicate in simple language, the nature of association between education and crime rate based on the least squares regression line.
4. [2+1+2+1=6] Plot the fitted line obtained in (2) on the scatterplot obtained in (1). Quantify the predictive ability of the line using a relevant measure and interpret the same. How much of the variation in crime rate remains unexplained ?
5. [2+2=4] Obtain point estimates of the following:
(a) The difference in mean crime rate for counties whose high school graduation rates differ by 5 percentage points.
(b) Mean crime rate in counties with high school graduation rate of X 91%.
6. [2+2+2=6] Obtain the 95% Wald confidence interval of the coefficient of education and interpret the same in the context of the problem. What does it imply about the significance of association between education and crime ?
7. [2+2+2+2=8] Suppose it is of interest to test whether counties with higher graduation rates have lower crime rate on an average. Carry out an appropriate hypotheses test to verify the above premise at α .05. State the hypotheses, test statistic, p-value and conclusion.
8. [2+2+2+2=8] Obtain the relevant residual plots corresponding to the fitted model and comment on the veracity of the linearity, homoscedasticity and normality assumptions. If any of these assumptions seem to have been violated, can you suggest any suitable transformation that would remedy the situation ?
9. [2+2+2+1+1=8] Randomly select 60 data points from the original data and fit the least squares regression line on this data (training data). Calculate the Root Mean Square Error (RMSE) for the fitted model on the training data. Now, implement this model on the remaining 24 data points (test data) and re-calculate the RMSE and for the test data. How does it
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