4. Explain the RESET test as a general test for functional form misspecification and discuss the drawbacks and advantages of this test. In your answer consider the following multiple linear regression model: V = 71+ 722 +73=3+ ti i= 1,.n,

4. Explain the RESET test as a general test for functional form misspecification and discuss the drawbacks and advantages of this test. In your answer consider the following multiple linear regression model: V = 71+ 722 +73=3+ ti i= 1,.n,

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.6: Higher-degree Polynomials And Rational Functions

Problem 1TU: The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t=...

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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?
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states, where xx is thousands of automatic weapons and yy is murders per 100,000 residents. xx 11.3 8.2 7.1 3.7 2.9 2.2 2.1 0.6 yy 13.9 10.7 10.3 7.2 6.5 5.6 5.5 4.6 Use your calculator to determine the equation of the regression line and write it in the y=ax+by=ax+b form. Round to 2 decimal places. According to this model, how many murders per 100,000 residents can be expected in a state with 4.6 thousand automatic weapons? Round to 3 decimal places. According to this model, how many murders per 100,000 residents can be expected in a state with 4.4 thousand automatic weapons? Round to 3 decimal places.
Consider the following population linear regression model of individual food expenditure: Y = 50 + 0.5X + u, where Y is weekly food expenditure in dollars, X is the individual’s age, and 50+0.5X is the population regression line. Suppose we generate artificial data for 3 individuals using this model. This artificial sample, which consists of 3 observations, is shown in the following table: Answer the following questions. Show your working. (a) What are the values of V1 and V4? (b) Suppose we know that in this artificial sample, the sample covariance between X and Y is 150, and the sample variance of X is 100. Compute the OLS regression line of the regression of Y on X. (Hint: Assume these summary statistics and the OLS regression line continue to hold in parts (c)-(e).) (c) What are the values of V5 and V7?
I have some doubts regarding linear regression. if any 2 variables in X1, X2 AND Y have a positive correlation, then in the linear regression Y = b0 + b1X1 +b2X2 +e, will the sign of b1 and b2 both be positive? will the residuals that we get from linear regression will always be uncorrelated given X?
he following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 100 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a)With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = Use technology to obtain the coefficient of correlation r. (Round your answer to three decimal places.) r =
Suppose a study wants to predict the market price of a certain species of turtle (Y) based on the following independent variables indicated in the table. Based from the table, what is the equation of the multiple linear regression? (Round off up to two decimal places. Market Price = 0.07 - 0.40*weight + 1.51*length + 1.41*width + 0.80*age Market Price = - 0.40*weight + 1.51*length + 1.41*width + 0.80*age Market Price = 0.07 + 0.40*weight + 1.51*length + 1.41*width + 0.80*age Market Price = 0.07 - 0.40 + weight + 1.51 + length + 1.41 + width + 0.80 + age
Suppose we want to predict job performance of mechanics based on mechanical aptitude test scores and test scores from personality test that measures conscientiousness. (a) Determine the regression equation. (b) Determine the SSE. Y X1 X2 1 40 25 2 45 20 1 38 30 3 50 30 2 48 28 3 55 30 3 53 34 4 55 36 4 58 32 3 40 34 5 55 38 3 48 28 3 45 30 2 55 36 4 60 34 5 60 38 5 60 42 5 65 38 4 50 34 3 58 38 Where Y is the Performance of the mechanics, X1 is the mechanical aptitude test and X2 is the personality test score that measure conscientiousness.
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.7 8.4 6.6 3.9 2.4 2.4 2.2 0.6 yy 14 10.9 9.4 7.5 6 5.8 5.8 4.4 xx = thousands of automatic weaponsyy = murders per 100,000 residents Use excel to determine the equation of the regression line. (Round to 2 decimal places)Determine the regression equation in y = b0 + bx(x) form and write it below. A) How many murders per 100,000 residents can be expected in a state with 10.7 thousand automatic weapons? B) How many murders per 100,000 residents can be expected in a state with 2.1 thousand automatic weapons?
The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 70 30 1995 130 40 110 40 2000 330 130 280 120 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = (b) Use technology to obtain the coefficient of correlation r. (Round your answer to three decimal places.) r =
A sixth-grade teacher believes that there is a relationship between his students’ IQscores (y) and the numbers of hours (x) they spend watching television each week. Thefollowing table shows a random sample of 7 sixth-grade students.y 125 116 97 114 85 107 105x 5 10 30 16 41 28 21 Does the data provide sufficient evidence to indicate that the simple linear regressionmodel is appropriate to describe the relationship between x and y? Perform a model utilitytest at α = 0.05. (Give H0, Ha, rejection region, observed test statistic, P-value, decisionand conclusion.)Find the Pearson sample correlation coefficient between x and y. Then interpretthe result.
Suppose that researchers are interested in determining the bi-annual salary of statisticians of different levels using their years of experience and their education level (M = bachelors, P = doctorate). They fit the following model to a dataset that includes these variables and, after performing the proper steps of multiple linear regression, the following multiple linear regression model is obtained: yˆ = 42308 + 323x1 + 213x2 + 301(x1*x2) where the variables are as follows: yˆ = predicted bi−annual salary in dollars, x1 = number of years of experiencex2= {1 if the education level is a doctorate 0 if the education level is a bachelors What is the predicted bi-annual salary in dollars of an employee with 5 years of experience and a bachelor’s degree?