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- For the data in problem 21, the
correlation between the number of crimes and population is r=0.933, whichmeans that r
2 = 0.8,7 (87%) istheproportion
of variance in the number of crimes that is predicted by popu1ation size. Does adding the amount spent on crime prevention as a second variable in the multiple regression equation add a significant amount tothe
Prediction? Testwith a= 0.05.
evaluate the relationship between the amount spent on crime prevention and the number of crimes crime while controlling population. It ispossible touse
multiple regression to accomplish essentially the same purpose. The data are as follows:
| Number of |
Crimes
- Findthemultipleregressionequationforpredict ing the number of crimes using the amount spent on prevention and population as the two predictor variables.
18. A researcher records the annual number of serious crime and the amount spent on crime prevention for several sma11 town, medium cities, and large cities across the country. The resulting data show a strong
prevention. However, the researcher suspectthat the positive correlation is actuallycaused by population as population increases, both the amount spent on crime prevention and the number of crimes will also increase. If population is controlled,there probably should be a
between crime rate and the amount spent on prevention.
| Number of |
Crimes
Size
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Chapter 16 Solutions
Statistics for The Behavioral Sciences (MindTap Course List)
- 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?arrow_forwardThe 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.arrow_forward
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