Problem 2 (12 points, 2 points each sub-question) 1. Consider only the Raise Percent variable for now, What is the median Raise Percent? Round to the nearest integer When a scatterplot of data points (zi, yi), i = 1,. .., n, displays a linear pattern, we can describe the overall pattern by drawing a straight line through the points. Fitting a line to data means drawing a line that comes as close as possible to the points. Let a denote the explanatory variable and y the response variable. Let a and y denote the mean of 21,. . ., T. and yl .., ya, respectively, Let 2. Consider only the Raise Percent variable. Is there any outlier? If so, point out which one. If s= and sy denote the corresponding standard deviations respectively. Let r denote the correlation. not, justify. The least-squares regression line of y on r is the line that minimizes the sum of the squares of the vertical distances of the data points from the line. The equation of the least-squares regression line is: 3. Briefly describe in words the relationship between Raise Percent and 2012-13 Salary in terms of its direction, strength, and form. where y is the predicted value of the response variable for a given value of r, where Sa bo = y - biz. 4. Suppose the mean salary is 120,000 and the standard deviation is 10,000. What is the mean Raise Percent? Here, bi is the slope, the amount by which y changes for each one-unit increase in z, and bo is the intercept, the value of y when z = 0. Consider the scatterplot of 16 individuals' 2012-13 salary in dollars and their raises in percent. 5. Which one of the following is the value of bj? Circle one and only one of the following answers: The linear regression line is also shown: (a) -0.0005, (b) -0.05, (c) -0.5, (d) 0, (e) 0.5, (f) 0.05, (g) 0.0005. 7- 6. What is the correlation r between the two variables? Circle one and only one of the following answers: (a) -10, (b) -1, (c) -0.9, (d) -0.5, (e) 0.1, (f) 0, (g) 0.1, (h) 0.5, (1) 0.9, () 1, (k) 10. Raise Percent A N 70000 80000 90000 100000 110000 120000 130000 140000 150000 160000 2012-13 Salary