Crime rate. A criminologist studying the relationship between level of education and crime rate in medium-sized U. S. counties collected data from a random sample of 84 counties; X is the percentage of individuals in the county having at least a high-school diploma, and Y is the crime rate last year. The data can be found on the course web page. Assume that the simple linear regression model is appropriate for this data.

a) Obtain the estimated regression function. Construct a scatterplot of the data and a plot of the fitted regression function on the same graph. Does the linear regression function appear to give a good fit here? Explain.
b) Obtain point estimates of the following:
i. the difference in the mean crime rate for two counties whose high-school graduation rates differ by one percentage point.
ii. the mean crime rate last year in counties with high school graduation per- centage X = 80 .
iii. E_10
iv. variance of the crime rate last year.

]
Y X
8487 74
8179 82
8362 81
8220 81
6246 87
9100 66
6561 68
5873 81
7993 74
7932 82
6491 75
6816 82
9639 78
4595 84
5037 82
4427 79
6226 78
10768 73
8335 77
12311 65
10104 77
10503 76
7562 79
8593 79
7133 78
10205 84
14016 78
5959 81
3764 89
4297 85
7562 77
4844 74
5777 80
3599 84
3219 88
11187 75
2105 77
6650 78
11371 61
4517 91
7348 83
5696 77
4995 85
9248 70
6860 88
9776 80
4280 82
11154 82
3442 82
9674 70
7309 64
4530 79
4017 83
7122 77
5689 76
6109 80
3343 84
5029 82
4330 81
5425 74
8769 81
6880 76
6538 78
6521 78
9423 79
9697 83
3805 79
3134 83
3433 81
2979 84
6836 64
5804 67
7986 75
10994 73
11322 77
8937 64
8807 75
11087 80
10355 83
7858 85
3632 91
8040 88
6981 83
7582 76
Use R-studio and give equations and worked out solutions. Please give out proper codes for r-studio

Refer to the data on crime rate in Problem 1.
a) Set up the ANOVA table and test whether there is a linear association between crime rate and percentage of high school graduates. What is estimated by the MSR in your ANOVA table? by MSE? Under what condition do MSR and MSE estimate the same quantity?
b) Suppose that the test in Part (a) is to be carried out by means of a general linear test. i. State the full and reduced models. ii. Obtain the error sum of squares (SSE) for both the reduced and full models and their degrees of freedom. iii. Compute the test statistic based on the general linear test approach. iv. Are the test statistics in Parts (a) and Part (b)(iii) numerically equivalent?