Q1. Correlation & Linear Regression:
The following data on sale price, size and land-to-building ratio for large industrial properties appeared in the paper "Using Regression Analysis in Real Estate Appraisal" (Appraisal journal [2002], 424-430):
|
Property
|
Sale Price (millions of dollars)
|
Size (thousands of sq. ft.)
|
Land-to-Building Ratio
|
|
1
|
10.6
|
2166
|
2.0
|
|
2
|
2.6
|
751
|
3.5
|
|
3
|
30.5
|
2422
|
3.6
|
|
4
|
1.8
|
224
|
4.7
|
|
5
|
20.0
|
3917
|
1.7
|
|
6
|
8.0
|
2866
|
2.3
|
|
7
|
10.0
|
1698
|
3.1
|
|
8
|
6.7
|
1046
|
4.8
|
|
9
|
5.8
|
1108
|
7.6
|
|
10
|
4.5
|
405
|
17.2
|
a. Calculate and interpret the value of the correlation coefficient between sale price and size (consider to use some software for the calculation).
b. Calculate and interpret the value of the correlation coefficient between sale price and land-to-building ratio (consider to use some software for the calculation).
c. If you wanted to predict sale price and you could use either size or land-to-building ratio as the basis for making predictions, which would you use? Explain.
d. Based on your choice in Part (c), find the equation of the least-squares regression line you would use for predicting y = sale price (consider to use some software to get the result).
Q2. Sampling Variability & Sampling Distributions
Newsweek (November 23, 1992) reported that 40% of all U.S. employees participated in "self-insurance" health plans (p=0.40).
a. In a random sample of 100 employees, what is the approximate probability that at least half of those in the sample participate in such a plan?
b. Suppose you were told that at least 60 of the 100 employees in a sample from your state participated in such a plan. Would you think p=0.40 for your state? Explain.
3. Confidence Level & Confidence Interval
The article "Hospitals Dispute Medtronic Data on Wires" (The Wall Street Journal, February 4, 2010) describes several studies of the failure rate of defibrillators used in the treatment of heart problems. In one study conducted by the Mayo Clinic, it was reported that failures were experienced within the first 2 years by 18 of 89 patients under 50 years old and 13 of 362 patients age 50 and older who received a particular type of defibrillator. Assume it is reasonable to regard these two samples as representative of patients in the two age groups who receive this type of defibrillator.
a. Construct and interpret a 95% confidence interval for the proportion of patients under 50 years old who experience a failure within the first 2 years after receiving this type of defibrillator.
b. Suppose that the researchers wanted to estimate the proportion of patients under 50 years old who experience a failure within the first 2 years after receiving this type of defibrillator to within 0.03 with 95% confidence. How large a sample should be used? Use the results of the study as a preliminary estimate of the population proportion.