Under Assumptions MLR.1 through MLR.4, E(B;) = B, for any value of Bj, j = 1, .., k: Bj is an a. unbiased estimator for Bj. Unbiasedness is a feature of the sampling distributions of ß; 's, which says nothing about the O b. estimates obtained from a given sample. It is always possible that one random sample, used to estimate (1), gives point estimates far from the true population parameters B;'s. Including one or more irrelevant variables in a multiple regression model, or overspecifying the c. model, does not affect the unbiasedness of the OLS estimators, but it can have undesirable effects of the variances of the OLS estimators. d. All of the above.

Under Assumptions MLR.1 through MLR.4, E(B;) = B, for any value of Bj, j = 1, .., k: Bj is an a. unbiased estimator for Bj. Unbiasedness is a feature of the sampling distributions of ß; 's, which says nothing about the O b. estimates obtained from a given sample. It is always possible that one random sample, used to estimate (1), gives point estimates far from the true population parameters B;'s. Including one or more irrelevant variables in a multiple regression model, or overspecifying the c. model, does not affect the unbiasedness of the OLS estimators, but it can have undesirable effects of the variances of the OLS estimators. d. All of the above.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter4: Linear Functions

Section4.3: Fitting Linear Models To Data

Problem 34SE: For the following exercises, consider this scenario: The profit of a company decreased steadily...

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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?
Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
For the following exercises, consider this scenario: The profit of a company decreased steadily overa ten-year spam.The following ordered pairs shows dollars and the number of units sold in hundreds and the profit in thousands ofover the ten-year span, (number of units sold, profit) for specific recorded years: (46,600),(48,550),(50,505),(52,540),(54,495). Use linear regression to determine a function Pwhere the profit in thousands of dollars depends onthe number of units sold in hundreds.
For the following exercises, consider the data in Table 5, which shows the percent of unemployed in a city ofpeople25 years or older who are college graduates is given below, by year. 41. Based on the set of data given in Table 7, calculatethe regression line using a calculator or othertechnology tool, and determine the correlationcoefficient to three decimal places.
For the following exercises, consider the data in Table 5, which shows the percent of unemployed ina city of people 25 years or older who are college graduates is given below, by year. 40. Based on the set of data given in Table 6, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to three decimal places.
For the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. Based on the set of data given in Table 5, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracy
Two variables, x and y are linearly related. The regression equation of y on x is y = 3.5 + 2.3x. One data point used to construct this regression equation is (5,17.5). What is the residual for this point and is the predicted value for x= 5 too small or too large? O A. 15, too small O B. -2.5, too large O C. 2.5, too large O D. -2.5, too small E. 2.5, too small