Consider the linear regression model Y; = Bo + Bị X; + U¡ and assume that E(Ui|X¡) = 0 for each i = 1, ..., n. Which one of the following is true about the interpretation of B1 ? a. Bi is the estimated average change in the value of Y; when we change the value of X; b. Bi is the predicted value of Y; Bi is the predicted value of Y; when X; = 0 d. Bi is the average change in the value of Y; when we change the value of X;
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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?What is the general formular for simple linear regression? * a) y = ßo + ß1x b) y = ß1 + ß0x c) none of the above d) both A and B
- According to the summary result of linear regression model between A and B obtained from R given below, we can fit a regression line. Assume thatA has any value. If we decrease the value of A by 3, how would Y be affected?a) 58.8945 decreaseb) 58.8945 increasec) 29.8827 increased) 49.5142 decreasee) 29.8827 decreaseAssume there is a positive linear correlation between the variable R (Return rate in percent of a financial investment) and the variable t (age in years of the investment) given by the regression equation R= 2.3t + 4.8 A. Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment? B. If the investment continues to grow at a constant rate, what is the expeted return rate when the investment is 7 years old? C. If the investment continues to grow at a constant rate, how old is the investment when the return rate is 30%?Which of the following statements are true regarding the simple linear regression modely=β0+β1 x1+ε1 A. εi is a nonrandom error. B. Β0 is the slope of the regression line. C. Β1 is the y-intercept of the regression line. D. yi is a value of the dependent variable (y) and xi is a value of the independent variable (x).
- The grades of a sample of 9 students on a prelim exam (x) and on the midterm exam (y) are shown below. Find the regression equation. y = 34.661 + 0.433x y = 0.777 + 12.0623x y = 12.0623 + 0.777x y = 34.661 - 0.433xin the regression specification y =α+βx +δz +ε, the parameter α is calledIf the general linear regression model is given by the equation: y = a + b?; considering the informationobtained in the attached figure, compute the value of a. A. 397.210 / B. 973.102 / C. 210.379 / D. 237.021
- Assume 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%?Using the table given, Which of the following is NOT necessarily true about the interpretation of the value of b in the simple linear regression equation y = a + bx for this problem? I. The monthly total costs will increase by $7.6437 for every one unit increase in the production volume. II. Since B > 0, there is a direct relationship between production volume and total costs. III. Because B > 1, there is a very strong positive linear relationship between production volume and total costs. a.) i and ii only b.) ii only c.) iii only d.) ii and iii onlyThe average gasoline price per gallon (in cities) and the cost of a barrel of oil are shown for a random selection of weeks from 2009–2010. Oil ($) 46.25 37.51 78.00 75.39 84.88 73.78 Gasoline ($) 2.197 2.182 2.987 3.015 3.109 3.000 Use the data to calculate, round your answers to 4 decimal places. Example 0.2345 or .2345 a) r = b) r2 = c) The linear regression equation is: y = x + d) According to your model, what is the average cost per gallon of gasoline if oil costs $60.00 per barrel? The cost is $ . (Round to the nearest cent)