4. What do you know about explained and unexplained variation? What is regression lineand regression equation?

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Answered: 4. What do you know about explained and…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 4GP

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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?
If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?
What is regression? why are there in general two regression lines? under what conditions properties of regression lines?
14.Calculate for the coefficient b in the linear regression equation describing the sample data below.
11. What is the standard error of the slope of the regression line (SEb)? Please put the answer in bold.
24) If the R-square value for a simple linear regression model is 0.80 and the regression line has anegative slope, the correlation coefficient describing the relationship between the two variables is_____________.
18)The regression equation is intended to be the “best fitting” straight line for a set of data. Whatis the criterion for “best fitting”?
What is the sample regression equation (round to 2 decimal places)? y = + Education + Experience + Age What is the hourly wage for a 30-year-old worker with 4 years of higher education and 3 years of experience (round to 2 decimal places)? Are any independent variables insignificant?
Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?
Define Residuals or errors in Alternative Regression Models?
Suppose there is a significant correlation between variables. describe 2 cases under which it might be inappropriate to use the linear regression equation for prediction
How can I calculate the different values in the equation y=ax+b for the regression line of a sample? How can I find the value for a and the value for b?

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4. What do you know about explained and unexplained variation? What is regression line and regression equation?