10 The variance of the prediction error is, a 41.8479 b 43.1422 c 44.4765 d 45.8520
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| 10 | The variance of the prediction error is, | |||
| a | 41.8479 | |||
| b | 43.1422 | |||
| c | 44.4765 | |||
| d | 45.8520 |
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4The 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?
- Consider the following scenario for Questions 6 through 9: The City of Bellmore’s police chief believes that maintenance costs on high-mileage police vehicles are much higher than those costs for low-mileage vehicles. If high-mileage vehicles are costing too much, it may be more economical to purchase more vehicles. An analyst in the department regresses yearly maintenance costs (Y) for a sample of 200 police vehicles on each vehicle’s total mileage for the year (X). The regression equation finds: Y = $50 + .030X with a r2 of .90 What is the IV? What is the DV? If the mileage increases by one mile, what is the predicted increase in maintenance costs? If a vehicle’s mileage for the year is 50,000, what is its predicted maintenance costs? What does an r2 of .90 tell us? Is this a strong or weak correlation? How can you tell?Question 4 The following table displays the mathematics test scores for a random sample of college students, along with their final SY16C grades. Fit the regression line y = a+bx to the data and interpret the results. Use the regression equation to determine the SY16C grade for a college student who scored 60 on their achievement test. What would their SY16C grade be? Mathematics test (x) SY16C grades (y) 1 39 65 2 43 78 3 21 52 4 64 82 5 57 92 6 47 89 7 28 73 8 75 98 9 34 56Question 21: Annual high temperatures in a certain location have been tracked for several years. Let XX represent the year and YY the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places).y = x + x y 1 11.41 2 11.02 3 11.73 4 11.94 5 13.45 6 10.56 7 10.47 8 12.08 9 12.19 10 13.5 11 12.41 12 10.52
- PARTS 3c-Question 3 only! For a sample of over 160 college students, the following variables were measured: Y = height X1 = mother’s height X2 = father’s height X3 = 1 if male, 0 if female The goal is to predict student’s height using the mother’s and father’s heights, and sex, where sex is categorized using the variable “male” = 1 if male, 0 if female. Question 1 The regression model is __________________________________________ Regress command results (remember that we now have n = 165 cases; we removed one outlier): Source | SS df MS Number of obs = 165 -------------+------------------------------ F( 3, 161) = 104.38 Model | 1679.17741 3 559.725803 Prob > F = 0.0000 Residual | 863.31653 161 5.36221447 R-squared = 0.6604 -------------+------------------------------ Adj R-squared = 0.6541 Total | 2542.49394 164 15.5030118…question 3 part 2 (thats the equation for the problem) The following estimated regression equation based on 10 observations was presented. ŷ = 21.1270 + 0.5508x1 + 0.4940x2 Here, SST = 6,736.125, SSR = 6,218.375, sb1 = 0.0815, and sb2 = 0.0561.Question #6 Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a flight. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet). Altitude 4 8 14 24 27 31 32 Temperature 55 37 20 −5 −27 −41 −57 a. Find the explained variation. ______________ (Round to two decimal places as needed.) b. Find the unexplained variation. _______________ (Round to five decimal places as needed.) c. Find the indicated prediction interval. _____________°F < y < ____________ °F (Round to four decimal places as needed.)
- Question 18 At a local club, the ages of the members and the times they took to run a 10 km race arerecorded. For a random sample of 25 club members aged between 27 and 60, their ages(x years) and times (y minutes) produce the following regression line. y = 0.83x + 41.28Four new members join the club. Their respective ages (in years) are 26, 18, 22, and 28. When therespective race times for the 4 new members are estimated, which one of these estimated race timesis the most reliable?A. 62.86 minutesB. 56.22 minutesC. 59.54 minutesD. 64.52 minutes Question 19 The data of the number of ‘centuries’ i.e. a scores of 100 runs or more, scored by players at acricket club during a season are given in the following table.Number of centuries Number of players0 41 k2 33 24 38 1Given that the mean number of centuries scored per player is 1.95, find the value of k.A. 7B. 3C. 4D. 1 Question 20The asking prices (in Rands) and the actual selling prices (in Rands), after bargaining, of 8commodities are…The following X and Y scores produce SSx=2 and SP=8. What is regression equation for predicting Y? X Y 1 2 2 3 3 10Question 27 In March, Maggie collected the daily sales of ice-cream in Montreal (Y) and the outdoor temperature for each day (X). She computed the sample correlation coefficient between X and Y to be 0.1, and used the data to build a simple linear regression model Y = b + cX.
