An experiment to study the relationship between x = time spent exercising (min) and y = amount of oxygen consumed during the exercise period resulted in the following summary statistics.Ex=x = 50 ΣΥ = 16,604 Σχι = 150n = 20Σy = 14,194,235 Σxy = 44,195(a) Estimate the slope of the population regression line.Estimate y intercept of the population regression line.(b) One sample observation on oxygen usage was 754 for a 2 min exercise period. What amount of oxygen consumption is predicted for this exercise period, and what is the corresponding residual?ŷ =residual(c) Calculate a 99% confidence interval for the average change in oxygen consumption associated with a 1 min increase in exercise time. (Use technology or SALT to calculate the critical value. Round your answers to three decimal places.)

From given data: n=20,∑x=50,∑y=16604,∑x2=150, ∑y2=14194235, ∑xy=44195,

Answered: (a) Estimate the slope of the…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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Olympic 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?
Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
If there is a positive correlation between X and Y, then the regression equation Y = bX + a will have _____.
Using a sample of recent university graduates, you estimate a simple linear regression using initial annual salary as the dependent variable and the graduate's weighted average mark (WAM) as the explanatory variable. If the regression model has an estimated intercept of 3200 and an estimated slope coefficient of 550, what is the predicted starting salary of a student with a WAM of 64?
A company has a set of data with employee age (X) and the corresponding number of annual on-the-job-accidents (Y). Analysis on the set finds that the regression equation is Y=60-0.5*X. What can be said of the correspondence (relation) between age and accidents? Are younger workers safer or more prone to accident? What is the likely number of accidents for someone aged 25?
A baseball enthusiast carried out a simple linear regression to investigate whether there is a linear relationship between the number of runs scored by a player and the number of times the player was intentionally walked. Computer output from the regression analysis is shown. Variable DF Estimate SE Intercept 1 16 2.073 Intentional Walks 1 0.50 0.037 R-sq=0.63R-sq=0.63 Let β1β1 represent the slope of the population regression line used to predict the number of runs scored from the number of intentional walks in the population of baseball players. A tt-test for a slope of a regression line was conducted for the following hypotheses. H0:β1=0Ha:β1≠0 below are the options provided thank you
Is the regression equation for predicting Y in terms of X the same as the regression line for predicting X in terms of Y?
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 slope of the population regression line?
In a simple linear regression model, the correlation coefficient between x and y is 0.8. What can you say about the strength and direction of the relationship between x and y?
Suppose that a regression relationship is given by the following:Y = β0 + β1X1 + β2X2 + εIf the simple linear regression of Y on X1 is estimated from a sample of n observations, the resulting slope estimate is generally biased for β1. However, in the special case where the sample correlation between X1 and X2 is 0, this will not be so. In fact, in that case the same estimate results whether or not X2 is included in the regression equation.a. Explain verbally why this statement is true.b. Show algebraically that this statement is true.
In a fisheries researcher's experiment, the correlation between the number of eggs in the nest and the number of viable (surviving) eggs for a sample of nests is r = 0.67. The equation of the regression line for number of viable eggs y versus number of eggs in the nest x is y = 0.72x + 17.07. For a nest with 140 eggs, what is the predicted number of viable eggs?
Suppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities: fragile, semi-fragile, and durable. Costs for 15 randomly chosen packages of approximately the same weight and same distance shipped, but of different cargo types, are provided in the file P14_16.xlsx. a. Estimate a regression equation using the given sample data, and interpret the estimated regression coefficients. b. According to the estimated regression equation, which cargo type is the most costly to ship? Which cargo type is the least costly to ship? c. How well does the estimated equation fit the given sample data? How might the fit be improved? d. Given the estimated regression equation, predict the cost of shipping a package with semi-fragile cargo.

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