Using XR17-07 data set
1)The term regression was originally used in 1885 by Sir Francis Galton in his analysis of the relationship between the heights of children and parents. He formulated the “law of universal regression,” which specifies that “each peculiarity in a man is shared by his kinsmen, but on average in a less degree.” (Evidently, people spoke this way in 1885.) In 1903, two statisticians, K. Pearson and A. Lee, took a random sample of 1,078 father—son pairs to examine Galton's law (“On the Laws of Inheritance in Man, I. Inheritance of Physical Characteristics,” Biometrika 2:457–462). Their sample regression line was
Son's height = 33.73 + .516 × Father's height
a. Interpret the coefficients.
b. What does the regression line tell you about the heights of sons of tall fathers?
c. What does the regression line tell you about the heights of sons of short fathers?
2) Using this Conduct the t-test of the coefficient of correlation to determine whether odometer reading and auction selling price are linearly related in Example 16.2. Assume that the two variables are bivariate normally distributed.
SOLUTION:
COMPUTE
MANUALLY:
The hypotheses to be tested are
H0: ρ = 0
H1: ρ ≠ 0
In Example 16.2, we found sxy = −2.909 and In Example 16.5, we determined that s2y = .300. Thus,
The coefficient of correlation is
The value of the test statistic is?a. What is the standard error of estimate? Interpret its value.
b. Describe how well the memory test scores and length of television commercial are linearly related.
c. Are the memory test scores and length of commercial linearly related? Test using a 5% significance level.
d. Estimate the slope coefficient with 90% confidence.
3) Construct a prediction interval and a confidence interval estimate of the expected value of the dependent variable for the given value of the independent variable. Use a 95% confidence level.
Using this 12* Are harder-working Americans more likely to urge to want government to reduce income differences? Test to determine whether there is sufficient evidence of a positive linear relationship between hours of work per week (HRS1) and position on whether government should reduce income differences (EQWLTH: 1 = Government should reduce income differences; 2, 3, 4, 5, 6, 7 = No government action). Find the position on the issue of whether government should reduce income differences of someone who works 50 hours per week.
4) Xr17-02 Pat Statsdud, a student ranking near the bottom of the statistics class, decided that a certain amount of studying could actually improve final grades. However, too much studying would not be warranted because Pat's ambition (if that's what one could call it) was to ultimately graduate with the absolute minimum level of work. Pat was registered in a statistics course that had only 3 weeks to go before the final exam and for which the final grade was determined in the following way:
Total mark = 20% (Assignment)
+ 30% (Midterm test)
+ 50% (Final exam)
To determine how much work to do in the remaining 3 weeks, Pat needed to be able to predict the final exam mark on the basis of the assignment mark (worth 20 points) and the midterm mark (worth 30 points). Pat's marks on these were 12/20 and 14/30, respectively. Accordingly, Pat undertook the following analysis. The final exam mark, assignment mark, and midterm test mark for 30 students who took the statistics course last year were collected.
5)Xr17-05 When one company buys another company, it is not unusual that some workers are terminated. The severance benefits offered to the laid-off workers are often the subject of dispute. Suppose that the Laurier Company recently bought the Western Company and subsequently terminated 20 of Western's employees. As part of the buyout agreement, it was promised that the severance packages offered to the former Western employees would be equivalent to those offered to Laurier employees who had been terminated in the past year. Thirty-six-year-old Bill Smith, a Western employee for the past 10 years, earning $32,000 per year, was one of those let go. His severance package included an offer of 5 weeks' severance pay. Bill complained that this offer was less than that offered to Laurier's employees when they were laid off, in contravention of the buyout agreement. A statistician was called in to settle the dispute. The statistician was told that severance is determined by three factors: age, length of service with the company, and pay. To determine how generous the severance package had been, a random sample of 50 Laurier ex-employees was taken. For each, the following variables were recorded:
Number of weeks of severance pay
Age of employee
Number of years with the company
Annual pay (in thousands of dollars)
a. Determine the regression equation.
b. Comment on how well the model fits the data.
c. Do all the independent variables belong in the equation? Explain.
d. Perform an analysis to determine whether Bill is correct in his assessment of the severance package.