a.
Find the least-squares regression line to predict the 15-year rates from 30-year rates.
a.
Answer to Problem 26E
The least-squares regression line to predict the 15-year rates from 30-year rates is
Explanation of Solution
Calculation:
The interest rates for the 30-year fixed-rate mortgages and the 15-year fixed-rate mortgages are given.
Denote the 30-year rates as x and the 15-year rates as y.
Least-squares regression:
For an ordered pairs of values of variables, (x, y) with respective means
Regression:
Software procedure:
Step by step procedure to obtain regression using Minitab software is given as,
- Choose Stat > Regression > Regression > Fit Regression Model.
- In Responses, enter the numeric column containing the response data y.
- In Continuous Predictors, enter the numeric column containing the predictor variable x.
- Choose Results, select Regression equation and click OK.
- Click OK.
Output using MINITAB software is given below:
From the output, the least-squares regression line for the data set is found to be
b.
Create a
b.
Answer to Problem 26E
The scatterplot with the least squares regression line on the same axes is given below:
Explanation of Solution
Calculation:
Scatterplot:
Software procedure:
Step-by-step procedure to obtain the scatterplot using the MINITAB software:
- Choose Graph > Scatterplot > With Regression, click OK.
- In Y variables, enter the column of y and in X variables, enter the column of x.
- Click OK.
c.
Explain whether it is possible to give an interpretation of the y-intercept of the regression line.
c.
Answer to Problem 26E
It is not possible to give an interpretation of the y-intercept of the regression line.
Explanation of Solution
Calculation:
Comparing the least-squares regression equation,
The y-intercept would mean that when the 30-year rate is
However, it is practically impossible for the rate of a fixed-rate mortgage to be 0 percent. The 30-year rate would always take some non-zero positive value.
Hence, it is not possible to give an interpretation of the y-intercept of the regression line.
d.
Find the predicted difference in the 15-year rates, if the 30-year rates differ by 0.3 percent.
d.
Answer to Problem 26E
The predicted difference in the 15-year rates, if the 30-year rates differ by 0.3 percent is 0.2682 percent.
Explanation of Solution
Interpretation:
It is known that when the predictor variable values differ by the amount d, the corresponding response variable values differ by amount
Here,
From part a, the least-squares regression equation is:
Comparing this equation with the general form of the regression equation,
Thus,
Hence, the predicted difference in the 15-year rates, if the 30-year rates differ by 0.3 percent is 0.2682 percent.
e.
Find the 15-year rate for a month which has 30-year rate is 3.5 percent.
e.
Answer to Problem 26E
The 15-year rate for a month which has 30-year rate is 3.5 percent is 2.7939 percent.
Explanation of Solution
Calculation:
From part a, the least-squares regression equation is:
For a quarterback whose 30-year rate is 3.5 percent,
Hence, the 15-year rate for a month which has 30-year rate is 3.5 percent is 2.7939 percent.
Want to see more full solutions like this?
Chapter 11 Solutions
Essential Statistics
- 9. The concentration function of a random variable X is defined as Qx(h) = sup P(x ≤ X ≤x+h), h>0. Show that, if X and Y are independent random variables, then Qx+y (h) min{Qx(h). Qr (h)).arrow_forward10. Prove that, if (t)=1+0(12) as asf->> O is a characteristic function, then p = 1.arrow_forward9. The concentration function of a random variable X is defined as Qx(h) sup P(x ≤x≤x+h), h>0. (b) Is it true that Qx(ah) =aQx (h)?arrow_forward
- 3. Let X1, X2,..., X, be independent, Exp(1)-distributed random variables, and set V₁₁ = max Xk and W₁ = X₁+x+x+ Isk≤narrow_forward7. Consider the function (t)=(1+|t|)e, ER. (a) Prove that is a characteristic function. (b) Prove that the corresponding distribution is absolutely continuous. (c) Prove, departing from itself, that the distribution has finite mean and variance. (d) Prove, without computation, that the mean equals 0. (e) Compute the density.arrow_forward1. Show, by using characteristic, or moment generating functions, that if fx(x) = ½ex, -∞0 < x < ∞, then XY₁ - Y2, where Y₁ and Y2 are independent, exponentially distributed random variables.arrow_forward
- 1. Show, by using characteristic, or moment generating functions, that if 1 fx(x): x) = ½exarrow_forward1990) 02-02 50% mesob berceus +7 What's the probability of getting more than 1 head on 10 flips of a fair coin?arrow_forward9. The concentration function of a random variable X is defined as Qx(h) sup P(x≤x≤x+h), h>0. = x (a) Show that Qx+b(h) = Qx(h).arrow_forward
- Suppose that you buy a lottery ticket, and you have to pick six numbers from 1 through 50 (repetitions allowed). Which combination is more likely to win: 13, 48, 17, 22, 6, 39 or 1, 2, 3, 4, 5, 6? barrow_forward2 Make a histogram from this data set of test scores: 72, 79, 81, 80, 63, 62, 89, 99, 50, 78, 87, 97, 55, 69, 97, 87, 88, 99, 76, 78, 65, 77, 88, 90, and 81. Would a pie chart be appropriate for this data? ganizing Quantitative Data: Charts and Graphs 45arrow_forward10 Meteorologists use computer models to predict when and where a hurricane will hit shore. Suppose they predict that hurricane Stat has a 20 percent chance of hitting the East Coast. a. On what info are the meteorologists basing this prediction? b. Why is this prediction harder to make than your chance of getting a head on your next coin toss? U anoiaarrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman