Concept explainers
In working further with the problem of exercise 4, statisticians suggested the use of the following curvilinear estimated regression equation.
- a. Use the data of exercise 4 to compute the coefficients of this estimated regression equation.
- b. Using α = .01, test for a significant relationship.
- c. Estimate the traffic flow in vehicles per hour at a speed of 38 miles per hour.
4. A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized.
where
y = traffic flow in vehicles per hour
x = vehicle speed in miles per hour
The following data were collected during rush hour for six highways leading out of the city.
- a. Develop an estimated regression equation for the data.
- b. Using α = .01, test for a significant relationship.
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Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
- The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02arrow_forwardDoes Table 1 represent a linear function? If so, finda linear equation that models the data.arrow_forwardOlympic 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?arrow_forward
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