When the errors in a regression model have AR(1) serial correlation, why do the OLS standard errorstend to underestimate the sampling variation in the B;? Is it always true that the OLS standard errorsare too small?

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 2AGP

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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?
Suppose the entering freshmen at a certain college have a mean combined SAT score of 1231 with a standard deviation of 122 In the first semester, these students attained a mean GPA of 2.64, with a standard deviation of 0.53. A scatterplot showed the association to be reasonably linear, and the correlation between SAT score and GPA was 0.47 How do i find the regression line using the equation
In linear regression, the mean value of all residuals will be greater for a correlation of -.70 than for a correlation of O -60 O.89 O -2 O.34
The fish in my pond have mean lenth 14 inches with a standard deviation of 2 inches and mean weight 4 pounds with a standard deviation of .8 pounds. The correlation coefficient of length and weight is .4. If the length of a particular randomly selected fish is reported to be 15 inches, then what should we predict for the weight of that fish using simple linear regression?
The fish in my pond have mean length 10 inches with a standard deviation of 2 inches and mean weight 4 pounds with a standard deviation of .6 pounds. The correlation coefficient of length and weight is .9. If the length of a particular randomly selected fish is reported to be 15 inches, then what should we predict for the weight of that fish using simple linear regression?
what is a confidence coefficinent for a simple linear regression line whoes alpha =0.05 and line is y(hat)=-7.45-10x
Suppose we have fit a multiple linear regression with 8 explanatory variables and an intercept with 85 observations. We want to test the joint significance of the first 5 explanatory variables using an F test. Please fill in the blanks for the numerator and denominator degrees of freedom of the F statistic of the test: "The F statistic is F(
What is the equation of the least square regression line for predicting the swimming speed of a beluga whale from its tail-beat frequency.
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In a partially destroyed laboratory, record of an analysis of correlation, data, the following results only are legible:Variance of X=9. Regression equation: 8X –10Y + 66=0, 40X–18Y = 214.(1) the mean value X and Y,(2) the correlation coefficient between X and Y, and (3) the standard deviation of Y ?
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find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. In each case, there is sujficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. Altitude and Temperature Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded by the author during Delta Flight 1053 from New Orleans to Atlanta. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet).

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When the errors in a regression model have AR(1) serial correlation, why do the OLS standard errors tend to underestimate the sampling variation in the B;? Is it always true that the OLS standard errors are too small?