I need someone to answer question 5 part b for me please. Thank you! 5. A crimin
ID: 3369839 • Letter: I
Question
I need someone to answer question 5 part b for me please. Thank you!
5. A criminologist is studying the relationship between level of education and overall crime rate and collected some data (columns C7 and C8 of hw2data.mtw) represented as a random sample of 84 geographic areas. Let X- the percent of individuals in the area having at least a high-school diploma, and let Y-crime rate (crimes reported per 100,000 residents). Assume that the model created satisfies the requirements of a valid linear model. a) Agovernment official wants to use this model to predict crime ina new area not in the original data set. Using the linear model you have created, estimate (if possible) the crime rate for this new area if X-50 percent of the individuals having at least a high-school diploma. If it is not theoretically possible to provide this estimate, please tell the government official why If X-50% Crime Rate 205 18-1 70.6 50% Crime Rate 11988 Fitted Line Plot CrimeRate 20518 170.6 PercentDiploma Rs 235629 17.0% 14000 R-Sq(adj) 16.0% 12000 8000 2000 60 65 70 75 85 95 PercentDiploma b) Provide evidence that the regression equation line passes through the point (Xhar.YBar). Is this always true? Explain. Note: Make certain you use as many significant digits possible for the slope and intercept estimates, not the rounded Minitah estimate given first. l The fitted regression line will always travel through the point that is the mean of X and the mean ofY Xhar Yhar) Because this is a property of the regression model.Explanation / Answer
Answer for (b) part only as specified in the question
Since the actual values of ybar and xbar are not available in the given data, it is not possible to illustrate the property that
the regression equation line passes through the point (xbar, ybar). ANSWER 1
Yes, the above property is true in general as shown below:
The equation of the estimated regression line is given by: ycap = ?0cap + ?1capx, …..(1)
where ?1cap = Cov(X, Y)/V(X) and ?0cap = ybar – ?1cap.xbar……………….….…..(2)
Substituting ?0cap = ybar – ?1cap.xbar from (2) and x = xbar in(1), we have:
ycap = ybar – ?1cap.xbar + ?1capxbar or
ycap = ybar.
=> The regression equation line passes through the point (xbar, ybar). Proved
DONE