Exam 15: Inferential Methods in Regression and Correlation

Decide, at the given significance level, whether the data provide sufficient evidence to conclude that x is useful forpredicting y. -Decide, at the 10% significance level, whether the data provide sufficient evidence to conclude that x is a useful predictor of y. 2 4 5 6 7 11 13 20 ywithhaton top equals3x

Is it possible for a sample linear correlation coefficient, r, to be close to 0 even though the population correlation coefficient, Ϭ, is close to 1? Explain your answer.

Perform the required correlation test for normality. -Twelve students were selected at random from a college class and were asked how many hours they had studied for a particular test. The results are as follows. 2.1 3.6 8.4 6.6 6.0 4.8 11.5 7.1 12.0 5.9 8.0 4.2 At the 5% significance level, do the data provide sufficient evidence to conclude that study times of students in this class are not normally distributed?

Perform the required correlation test. You may presume that the assumptions for regression inferences are met. -A set of sample data consisting of 19 pairs of x and y values yields a sample linear correlation coefficient of -0.887. At the 1% significance level, do the data provide sufficient evidence to conclude that x and y are negatively linearly correlated?

Perform the required correlation test. You may presume that the assumptions for regression inferences are met. -The sample data below are the index of exposure (x)to radioactive waste for nine different Oregon counties and cancer mortality rate (y)(deaths per 100,000). 2.49 2.57 3.41 1.25 1.62 3.83 11.64 6.41 8.34 147.1 130.1 129.9 113.5 137.5 162.3 207.5 177.9 210.3 The sample linear correlation coefficient is r = 0.926. At the 5% significance level, do the data provide sufficient evidence to conclude that index of exposure and cancer mortality rate are linearly correlated?

Perform the required correlation test. You may presume that the assumptions for regression inferences are met. -Ten students in a graduate program were randomly selected. Their grade point averages (GPAs)when they entered the program were between 3.5 and 4.0. The following data consist of the students' GPAs (x)on entering the program and their current GPAs (y). x 3.5 3.8 3.6 3.6 3.5 3.9 4.0 3.9 3.5 3.7 3.6 3.7 3.9 3.6 3.9 3.8 3.7 3.9 3.8 4.0 The sample linear correlation coefficient is r = 0.043. At the 5% significance level, do the data provide sufficient evidence to conclude that entering GPA and current GPA are linearly correlated?

Construct a normal probability plot of the residuals for the given regression data. - 3 2 4 8 4 6 ywithhaton top equals3plusx

The sample data below are the index of exposure (x)to radioactive waste for nine different Oregon counties and cancer mortality rate (y)(deaths per 100,000). 2.49 2.57 3.41 1.25 1.62 3.83 11.64 6.41 8.34 147.1 130.1 129.9 113.5 137.5 162.3 207.5 177.9 210.3 =114.72+9.23x A 99% confidence interval for the slope of the population regression line that relates cancer mortality rate to index of exposure is 4.26 to 14.20. Provide an interpretation of this confidence interval.

Decide, at the given significance level, whether the data provide sufficient evidence to conclude that x is useful forpredicting y. -Decide, at the 10% significance level, whether the data provide sufficient evidence to conclude that x is a useful predictor of y. x 0 1 5 3 3 y 7 5 -4 0 1 ywithhaton top equals7point105minus2point211x

Decide, at the given significance level, whether the data provide sufficient evidence to conclude that x is useful forpredicting y. -Decide, at the 10% significance level, whether the data provide sufficient evidence to conclude that x is a useful predictor of y. 3 2 4 ywithhaton top equals3plusx

If the assumptions for regression inferences are met, what would you expect to see when constructing a residual plot and a normal probability plot for the residuals?

The heights (in inches)of a random sample of students from one college are as follows. 67 61 65 70 66 60 66 68 62 64 At the 1% significance level, do the data provide sufficient evidence to conclude that heights of students at this college are not normally distributed?

Perform the required correlation test for normality. -The data below represent the weekly salaries (in dollars)of ten employees selected randomly from a particular company. 450 1035 500 1050 460 1125 480 1256 560 1470 At the 10% significance level, do the data provide sufficient evidence to conclude that weekly salaries of employees at this company are not normally distributed?

Construct a residual plot for the given data. - 3 2 4 8 4 6 ywithhaton top equals3plusx

Perform the required correlation test for normality. -At one bank, twelve customers were selected at random as they entered the bank and asked to record how long they spent waiting in line. The times (in minutes)were as follows. 6.9 3.0 5.1 1.5 2.7 7.0 6.8 2.4 6.2 1.2 3.8 4.2 At the 5% significance level, do the data provide sufficient evidence to conclude that waiting times of customers at this bank are not normally distributed?

Decide, at the given significance level, whether the data provide sufficient evidence to conclude that x is useful forpredicting y. -Applicants for a particular job, which involves extensive travel in Spanish speaking countries, must take a proficiency test in Spanish. The sample data below were obtained in a study of the relationship between the numbers of years applicants have studied Spanish (x)and their score on the test (y). 3 4 4 2 5 3 4 5 3 2 57 78 72 58 89 63 73 84 75 48 =31.55+10.90x The standard error of the estimate is approximately 5.651. At the 5% level of significance, do the data provide sufficient evidence to conclude that the slope of the population regression line is not 0 and hence that number of years of study is useful as a predictor of score on the test?

In the context of regression analysis, which of the following, roughly speaking , does the standard error of the estimate give an indication of?

In a study of the relationship between height and weight, a sample regression equation is obtained in which height is used as the predictor variable. Explain why a confidence interval for a conditional mean corresponding to the height 70 inches is narrower than a prediction interval corresponding to the height 70 inches.

Paired sample data is given. Discuss what it would mean for Assumptions 1-3 for regression inferences to be satisfied bythe variables under consideration. -A social scientist is interested in the relationship between years of education and income in adults in the U.S. A random sample of nine working adults yields the following data, where x denotes years of education completed and y denotes annual income in thousands of dollars. 10 11 17 15 14 12 11 11 15 20.5 17.4 54.8 44.2 33.9 66.2 19.3 34.5 32.8

Paired sample data is given. Discuss what it would mean for Assumptions 1-3 for regression inferences to be satisfied bythe variables under consideration. -A social scientist is interested in the relationship between age and income in adults aged 20-60. A random sample of eight adults yields the following data, where x denotes age in years and y denotes annual income in thousands of dollars. 27 55 48 25 31 44 57 35 18.9 48.3 27.6 33.2 19.6 65.0 55.6 20.1