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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?Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. First Down The following table shows the probability P, as a percentage, of a college football team converting on fourth down when not goal to go versus the distance D, in yards, to the first down maker. 28 D = distance, in yards P = probability 1 70 2 60 3 53 4 46 5 41 6 37 7 34 8 32 a.Use exponential regression to model the data. b.Plot the data along with the exponential model. c.What probability does the model give of gaining a first down for fourth down and 10yards to go? Note: the actual probability is 28.Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Medicare ExpendituresThe following table is from the Centers for Medicare that is, M=1000?
- Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?An experiment is run. The mass of an object is recorded over time. Time (min) Mass (g) 11 35 12 11 13 7 16 7 41 7 Using your calculator, run a linear regression to determine the equation of the line of best fit. Round to two decimal places, use x for the variable.y= I attempted 20.28 +0.37 but that was inncorrectComplete the missing information for this regression model. Note: N=26N=26. (Except for P-values, report all values accurate to 3 decimal places. For P-values, report accurate to 4 decimal places.) ˆYY^ = 26.759 + 0.818X10.818X1 −- 2.999X22.999X2 + X3X3 2.382 0.547 1.674 0.734 Standard Errors 11.234 1.495 t-ratios 0.0991 P-values
- A researcher conducted a number of descriptive statistics for two variables X and Y. They were as follows: SP = -20; SSx = 4; My = 7; Mx = 3 What is b equal to? What is a equal to? Using b and a construct a regression equation, and then using the regression equation, calculate the value of predicted Y when X = 2?A new computer circuit was tested and the times (in nanoseconds) required to carry out different subroutines were recorded. Difficulty 1 3 3 4 5 6 6 6 Time 10 11 12 9 15 19 21 18 Find the regression line for the data. Assume x is the difficulty level and y is the time. (Round your values to four decimal places.)You have obtained a sub-sample of 1744 individuals from the Current Population Survey (CPS) and are interested in the relationship between weekly earnings and age. The regression, using heteroskedasticity-robust standard errors, yielded the following result: = 239.16 + 3.75× Age, R2 = 0.15, SER = 287.21., where Earn and Age are measured in dollars and years respectively. Interpret the intercept? Interpret the slope coefficient b) Is the effect of age on earnings large? The average age in this sample is 37.5 years. What is annual income in the sample? (e) Interpret the measures of fit.
- A surgery intern has conducted a study of the sleeping habits of her colleagues and has developed a following regression equation: y-hat = 6 + 0.1X, where X is the number of hours working on one shift, and Y is the number of hours sleeping at night after that shift. Yvette worked 10 hours and slept 8 hours. What is Yvette’s residual? 0.1 1 6 7Which 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 aboveConsider the following multiple regression results for estimation of demand for coffee: Dc= 6.27+0.48DI-1.23Pc-3.5Pt+0.19Pm+0.07Ae. Where, Dc=Demand for coffee (in ‘000 dollars) DI=Disposable income Pc=Price index of coffee Pt=Price index of tea Pm=Price index of milk Ae=Advertising expenditure (in ‘000 dollars) Adjusted R square=0.90 Comment on the results including signs and coefficients of the multiple regression..