4. Can the speed of a vehicle be predicted by the age of its driver? The speeds Y (inkm/h) of a sample of ten vehicles are recorded, along with the ages X of their drivers.From the data, we calculate i = 48.2, j = 107.8, (z:-2)² = 3669.6, (4- û)° =752.7. The least squares regression line is calculated to be ŷ = 133.198 – 0.527x.It is also determined that 57.5% of the variation in the speed of a vehicle can beaccounted for by its regression on the age of the driver.(a) What is the value of the correlation between the age of a driver and the speedof a vehicle?(b) Provide an interpretation of the slope of the least squares regression line.(c) Calculate a 95% confidence interval for the parameter 31 in the simple linearregression model.(d) We would like to conduct a hypothesis test at the 5% level of significance todetermine whether a linear relationship exists between the age of a driver andthe speed of a vehicle. Could the confidence interval in (c) have been usedto conduct the test? Why or why not? If it could be used, what would theconclusion be, and why?

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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?
8)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.86, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 86000 and the sum of squared errors (SSE) is 14000. From this information, what is MSE/MST? .5000 NONE OF THE OTHERS .2000 .3000 .4000
A set of paired data has a least squares regressionline with equation yn = 0.50x + 2.0 and a correlationcoefficient of r = 0.80. Suppose we convert the datafor each variable to z-scores and then compute the newregression line. What will the equation be?A) zˆy = 0.50zx B) zˆy = 0.64zxC) zˆy = 0.80zx D) zˆy = 0.50zx + 20E) zˆy = 0.80zx + 20
The least-squares regression line relating two statistical variables is given as = 24 + 5x. Compute the residual if the actual (observed) value for y is 38 when x is 2. 4 38 2
Given are five observations for two variables, x and y. xi 3 8 12 18 20 yi 54 57 50 24 11 -select your answer choices- b. The least squares line provided an (good, bad) fit; __ % of the variability in y has been explained by the estimated regression equation (to 1 decimal)
9)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.79, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 79000 and the sum of squared errors (SSE) is 21000. From this information, what is the adjusted R-square? .8 .7 NONE OF THE OTHERS .6 .5
A researcher collected data on the cholesterol level, CC, and the age, AA, of 24 people selected at random. Using the data, the researcher calculated the least-squares regression line to be Cˆ=182+2.2AC^=182+2.2A and the standard error of the slope to be 0.38. If the conditions for inference are met, which of the following is closest to the value of the test statistic to test the hypotheses H0:β=0H0:β=0 versus Ha:β≠0Ha:β≠0 ?
Suppose that a least squares regression line equation is ˆy = 1.65 − 2.20x and the actual y value corresponding to x = 10 is −19, what is the residual value corresponding to y = −19?
1. Prior to being hired, the ve salespersons for a computer store were given a standard sales aptitude test. For each individual, the score achieved on the aptitude test and the number of computer systems sold during the first 3 months of their employment are shown in the attached image. (a) Determine the least-squares regression line and interpret its slope. (b) Estimate, for a new employee who scores 60 on the sales aptitude test, the number of units the new employee will sell in her first 3 months with the company. (c) Find the standard error of estimate. (d) Find the r-square of the model.
A financial analyst is examining the relationship between stock prices and earnings per share. She chooses sixteen publicly traded companies at random and records for each the company's current stock price and the company's earnings per share reported for the past 12 months. Her data are given below, with x denoting the earnings per share from the previous year, and y denoting the current stock price (both in dollars). Based on these data, she computes the least-squares regression line to be ŷ =−0.2390+0.044x. This line, along with a scatter plot of her data, is shown below.
17) Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 41 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.9, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 10000. From this information, what is the number of degrees of freedom for the t-distribution used to compute critical values for hypothesis tests and confidence intervals for the individual…
Suppose that the sales of a company (Y) is regressed on advertising expenditure (x) and labor cost (z), and the estimated regression equation is Y = 5 + 0.5x + 0.7z + u (where u is the error term). Here, sales, advertising expenditure and labor cost are measured in million Tk. Standard error for the coefficient of x is 0.04, standard error for the coefficient of z is 0.01, and the sample size is 20. Can we conclude that advertising expenditure is a statistically significant variable?

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