An Introduction to Mathematical Statistics and Its Applications (6th Edition)
6th Edition
ISBN: 9780134114217
Author: Richard J. Larsen, Morris L. Marx
Publisher: PEARSON
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Chapter 11.3, Problem 7Q
To determine
A 90% confidence interval for the y-intercept
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Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet.
The decrease in blood pressure y will vary about this subpopulation mean. What is the distribution of y for this subpopulation?
Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet.
What is the subpopulation mean when x = 7 servings per day?
A set of n = 25 pairs of X and Y values has a correlation of r = -0.50 with SSX = 38 and SSY = 14.
Find the standard error of estimate for the regression equation.
What percentage of the variance in Y is accounted for by X?
Chapter 11 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 11.2 - Crickets make their chirping sound by sliding one...Ch. 11.2 - The aging of whisky in charred oak barrels brings...Ch. 11.2 - Prob. 3QCh. 11.2 - Prob. 4QCh. 11.2 - Prob. 5QCh. 11.2 - Prob. 6QCh. 11.2 - The relationship between school funding and...Ch. 11.2 - (a) Find the equation of the least squares...Ch. 11.2 - Prob. 9QCh. 11.2 - Prob. 10Q
Ch. 11.2 - Prob. 11QCh. 11.2 - Verify that the coefficients a and b of the least...Ch. 11.2 - Prob. 13QCh. 11.2 - Prob. 14QCh. 11.2 - Prob. 15QCh. 11.2 - Prob. 16QCh. 11.2 - Prob. 17QCh. 11.2 - A graph of the luxury suite data in Question 8.2.5...Ch. 11.2 - Set up (but do not solve) the equations necessary...Ch. 11.2 - Prob. 20QCh. 11.2 - The growth of federal expenditures is one of the...Ch. 11.2 - Prob. 22QCh. 11.2 - Prob. 24QCh. 11.2 - Prob. 25QCh. 11.2 - Among mammals, the relationship between the age at...Ch. 11.2 - Prob. 27QCh. 11.2 - Years of experience buying and selling commercial...Ch. 11.2 - Prob. 29QCh. 11.2 - The following table shows a portion of the results...Ch. 11.3 - Insect flight ability can be measured in a...Ch. 11.3 - The best straight line through the Massachusetts...Ch. 11.3 - Based on the data in Question 11.2.1, the...Ch. 11.3 - Suppose an experimenter intends to do a regression...Ch. 11.3 - Prob. 5QCh. 11.3 - Prob. 6QCh. 11.3 - Prob. 7QCh. 11.3 - Set up and carry out an appropriate hypothesis...Ch. 11.3 - Test H0:1=0 versus H1:10 for the plumage...Ch. 11.3 - Prob. 10QCh. 11.3 - Derive a formula for a 95% confidence interval for...Ch. 11.3 - Which, if any, of the assumptions of the simple...Ch. 11.3 - Prob. 13QCh. 11.3 - Construct a 90% confidence interval for 2 in the...Ch. 11.3 - Regression techniques can be very useful in...Ch. 11.3 - Construct a 95% confidence interval for E(Y2.750)...Ch. 11.3 - Prob. 18QCh. 11.3 - The fuel economy (in miles per gallon) of an...Ch. 11.3 - In the radioactive exposure example in Question...Ch. 11.3 - Attorneys representing a group of male buyers...Ch. 11.3 - Prob. 23QCh. 11.3 - Show that i=1n(YiY)2=i=1n(YiYi)2+i=1n(YiY)2 for...Ch. 11.4 - Prob. 1QCh. 11.4 - Prob. 2QCh. 11.4 - Prob. 3QCh. 11.4 - Prob. 4QCh. 11.4 - Prob. 5QCh. 11.4 - Let the random variable X take on the values...Ch. 11.4 - Prob. 7QCh. 11.4 - Prob. 8QCh. 11.4 - Prob. 9QCh. 11.4 - Prob. 10QCh. 11.4 - Some baseball fans believe that the number of home...Ch. 11.4 - Many people believe that a salary bonus is a...Ch. 11.4 - The extent to which stress is a contributing...Ch. 11.4 - Burglary and larceny both involve the illegal...Ch. 11.4 - A common saying in golf is You drive for show, but...Ch. 11.5 - Suppose that X and Y have a bivariate normal pdf...Ch. 11.5 - Suppose that X and Y have a bivariate normal...Ch. 11.5 - Prob. 3QCh. 11.5 - Suppose that the random variables X and Y have a...Ch. 11.5 - Prob. 5QCh. 11.5 - Give conditions on a0,b0, and u so that...Ch. 11.5 - Prob. 7QCh. 11.5 - In a study of heart disease (79), the weight (in...Ch. 11.5 - Prob. 9QCh. 11.5 - Prob. 10QCh. 11.5 - The National Collegiate Athletic Association has...
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- Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.arrow_forwardFind the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardOlympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forward
- One of the residuals in a linear regression model is equal to 6.5. Other results from the model areMSE = 3.2, MSR = 4.5, SSE = 182, and SSR = 243. The value of the standardized residual is:a. 3.06b. 3.63c. 0.48d. 0.42e. None of the other answers is correctarrow_forwardConsider the equation of the regression line y = 25 – 2.5x and ỹ = 12, %3D Find y when x = 6 assuming the linear correlation is not significant. %3Darrow_forwardNine data points of data yield r=0.867 and the regression equation y=19.4+0.93x. Also, y=64.7. What is the best predicted value of y for x=40?arrow_forward
- A set of n = 15 pairs of X and Y values has a correlation of r = +0.80 with SSY = 75, and the regression equation for predicting Y is computed. Find the standard error of estimate for the regression equation. How big would the standard error be if the sample size were n = 30.arrow_forwardYou are studying how a penguin's flipper length (in mm) explains its body mass (in grams) using linear regression. You choose a non-directional alternative to be safe. Your t* = 32.56 and the non-directional p-value is 0.000000034. Indicate your statistical decision below. O Fail to reject Ho because p > alpha O Reject Ho because p alphaarrow_forwardPlease do not give solution in image formate thanku. i am stuck on this question.. You run a regression analysis on a bivariate set of data ( n = 34 ). You obtain the regression equation y = - 2.112 x + 59.334 with a correlation coefficient of r = - 0.878 (which is significant at α = 0.01 ). You want to predict what value (on average) for the explanatory variable will give you a value of 70 on the response variable. What is the predicted explanatory value? x = (Report answer accurate to one decimal place.)arrow_forward
- For 40 eruptions of the Old Faithful geyser in Yellowstone National Park, duration times (sec) were recorded along with the heights (ft) of the eruptions. The linear correlation coefficient is r = 0.0915 and the regression equation is = 119 + 0.0331x, where x represents duration time. The mean of the 40 duration times is 245.0 sec and the mean of the 40 heights is 127.2 ft. What is the best predicted height of an eruption with a duration time of 120 min?arrow_forwardOne set of 20 pairs of scores, X and Y values, produces a correlation of r = 0.70. If SSY = 150, calculate the standard error of the estimate for the regression linearrow_forwardA regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).The results of the regression were:y=ax+b a=-1.38 b=39.555 r2=0.693889 r=-0.833 Assume the correlation is significant, and use this to predict the number of situps a person who watches 7 hours of TV can do (to one decimal place)arrow_forward
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