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- 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.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?Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
- .The worker has noticed that the more time he spends at work (x), the less money he is likely to make (y) in conducting transactions for his firm. Which of the regression equations MOST suggests such a possibility?The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.7 8.6 6.7 3.5 2.3 2.6 2.2 0.7 yy 14 11 10 7 6.1 6.4 5.9 4.3 xx = thousands of automatic weaponsyy = murders per 100,000 residentsDetermine the regression equation in y = ax + b form and write it below. (Round to 2 decimal places) A) How many murders per 100,000 residents can be expected in a state with 6.5 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 11 thousand automatic weapons? Answer = Round to 3 decimal places.the table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.6 8.6 7 3.5 2.9 2.2 2.3 0.6 yy 14.2 11.4 9.7 7.2 6.6 5.9 5.7 4.3 x = thousands of automatic weaponsy = murders per 100,000 residentsDetermine the regression equation in y = ax + b form and write it below. (Round to 3 decimal places) A) How many murders per 100,000 residents can be expected in a state with 6.2 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 3.8 thousand automatic weapons? Answer = Round to 4 decimal places.
- 2.state each of the five assumptions of the classical regression model (OLS) and give an intuitive explanation of the meaning and need for each of themAssume that there is a positive linear correlation between the variable R (return rate in percent of financial investment) and the variable t (age in years of the investment) given by the regression equation R = 2.5t + 5.3. 1- Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment? 2- If the investment continues to grow at a constant rate, what is the expected return rate when the investment is 7 years old? 3- If the investment continues to grow at a constant rate, how old is the investment when the return rate is 32.8%?If other factors are held constant, if the Pearson correlation between X and Y is r = 0.50, then the regression equation will produce more accurate predictions than would be obtained if r = 0.70. True or false?
- If the general linear regression model is given by the equation: y = a + b?; considering the informationobtained in Figure 2 above, compute the value of a.(a) For United States, provide data for the variables below over the years 1993 –2007:(i) Net migration rate (per 1,000 population)(ii) Total fertility rate (live births per woman)(iii)Unemployment, general level (Thousands)(iv) Wages(v) Life expectancy at birth for both sexes combined (years)Data can be obtained from the UN database http://data.un.org/Explorer.aspxUsing R-Studio, estimate a regression equation to determine the effect of unemployment,general level, wages and life expectancy at birth for both sexes on the net migration rate.(All codes and regression output should be provided).(i) Write down the regression equation. (ii) Interpret the coefficients and determine which of the individual coefficients in theregression model are statistically significant. In responding, construct and test anyappropriate hypothesis. (iii) Interpret the coefficient of determination.a) For United States, provide data for the variables below over the years 1993 – 2007: (i) Net migration rate (per 1,000 population) (ii) Total fertility rate (live births per woman) (iii)Unemployment, general level (Thousands) (iv) Wages (v) Life expectancy at birth for both sexes combined (years) Data can be obtained from the UN database http://data.un.org/Explorer.aspx Using R-Studio, estimate a regression equation to determine the effect of unemployment, general level, wages and life expectancy at birth for both sexes on the net migration rate. (All codes and regression output should be provided).(i) Write down the regression equation. (ii) Interpret the coefficients and determine which of the individual coefficients in theregression model are statistically significant. In responding, construct and test anyappropriate hypothesis. (iii) Interpret the coefficient of determination. (iv) Using the 10% level of significance, determine and discuss whether the overallregression equation…
