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We are asked to find the regression line
Step by step
Solved in 2 steps
- 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?The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.If the standard error of the estimate for a regression model fitted to a large number of paired observations is 1.75, approximately 95% of the residuals would lie within ______. −3.50 and +3.50 −1.75 and +1.75 −0.95 and +0.95 −0.68 and +0.68 −0.97 and +0.97
- Which of the following does not need to be computed to determine a simple regression line? SSx SP "Y-hat" SSyUsing the regression line attached. Based on only the above plot, one can conclude: a) height causes an increase in weight b) weight causes an increase in height c) taller people are more likely to weigh more than shorter people, at least in the sample on which this data is based d) a statistically significant predictive relationship between height and weight e) c and dThe following data shows the dexterity test scores of five assembly-line employees of Dimples Company Limited and their respective hourly productivity.Employee Score on dexterity test (?) Ali 12Kofi 14Kwesi 17Abudu 16Nana 11Units produced in an hour (?) 55636770 51You are required to(i) Write the regression equation(ii) Interpret the regression equation(iii) Calculate the Pearson’s Product Moment Correlation Coefficient.(iv) Interpret the correlation coefficient (v) Suppose the dexterity test score is 13, what would be the units produced in an hour? (vi) Clearly explain (in detail) the difference between regression analysis and correlation analysis.
- Consider the following hypothetical regression, with FAIL? as a dummy variable for if a business failed in its first year (1=failed, 0=didn’t fail); LOAN is how much money, in thousands of dollars, the business got as a loan when it started; GIG? is a dummy variable for if there was a gig economy job available, such as driving for Lyft (1=available, 0=not available), and COMP is the number of existing competitors the business faced when it started. All variables are statistically significant. FAIL? = 0.63 – 0.01*LOAN – 0.08*GIG? + 0.05*COMP Answer the following: Determine the predicted value of FAIL? if the business had a $30,000 loan, there was no gig economy, and four competitors. In everyday language, what does the estimated value found in A mean? If a business gets an additional six thousand dollars in loans, how would FAIL? change? Give the “punchline” interpretation of the COMP variable: “For every additional competitor…”Consider the following table of N=3 observations. Calculate estimates of b1 and b0 (b-hat) considering the linear regression model y=b+b*x Compute SSE for this regression Assume that SST=32. What is R^2 for this regression?In the following model, "employed" is a dummy indicating a person is employed: donation = B + B edu + Bemployed + uT Running this model will produce the same results of differential in donation between employed people and unemployed people as running two separate regressions for employed people and unemployed people. A. True B. False
- Which of the following best describes a regression coefficient in a bivariate setting? a. The change in Y predicted by a unit change in X b. The slope of a line that minimizes the sum of squared residuals c. The correlation coefficient multiplied by SDy/SDx d. All of the aboveBased on the data shown below, calculate the regression line (each value to at least two decimal places)y = x + x y 2 19.55 3 18.7 4 19.25 5 17.3 6 19.85 7 18.9 8 18.85 9 18.3 10 15.35 11 16.2 12 18.35 13 14.7The following data is a regression model where the U.S. Department of Transportation has tried to relate the rate of fatal traffic accidents (per 1000 licenses) to the percentage of motorists under the age of 21. Data has been collected for 42 major cities in the United States. SUMMARY OUTPUT Regression Statistics Multiple R 0.83938748 R Square 0.70457134 Adjusted R Square 0.69718562 Standard Error 0.58935028 Observations 42 ANOVA df SS MS F Regression 1 33.13441764 33.1344 95.3964 Residual 40 13.89335048 0.34733 Total 41 47.02776812 Coefficients Standard Error t Stat P-value Intercept -1.5974138 0.371671454 -4.2979 0.00010 Percent Under 21 0.28705317 0.029389769 9.76711 3.79E-9…