?, known as the Classical Linear Regression Model (CLRM), where y is the dependent variable, X is the set of independent variables, ? is the vector of parameters to be estimated and ? is the error term. Present and discuss the R2 and the adjusted R2. Discuss pros and cons of each of the two statistics.

?, known as the Classical Linear Regression Model (CLRM), where y is the dependent variable, X is the set of independent variables, ? is the vector of parameters to be estimated and ? is the error term. Present and discuss the R2 and the adjusted R2. Discuss pros and cons of each of the two statistics.

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?
Consider the following model:? = ?? + ?,known as the Classical Linear Regression Model (CLRM), where y is the dependent variable, X is the set of independent variables, ? is the vector of parameters to be estimated and ? is the error term.a) List and discuss the assumptions that make the Ordinary Least Squares (OLS) the Best Linear Unbiased Estimator (BLUE).b) Derive the OLS estimator and variance and discuss where each assumption is needed for the derivation of the two parameters.c) Discuss the properties of linearity, unbiasedness, and efficiency, andwhat assumption you need for each of these properties to hold.d) Present and discuss the R2 and the adjusted R2 Discuss pros and cons of each of the two statistics.
Which of the multivariate regression parameters listed below would be best interpreted as: the predicted value on the dependent variable when all of the independent variables in the model are equal to zero. a b1 X1 R2
Given a regression equation ?) = 2.35 + 6.82x, with n = 18 and a correlationcoefficient, r = 0.42, conduct a hypothesis test to determine if the regressionrelationship between x and y is statistically significant at the 2% level ofsignificance. What conclusion can be drawn from the hypothesis test?
Consider the following five data points: X -1 0 1 2 3 Y -1 1 2 4 5 a. Use regression analysis to calculate by hand the estimated coefficients of the equation Y = B + aX. b. Compute the standard error and the t-statistics for the coefficient of X.
In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the midterm exam. The equation of the least‑squares regression line was ?̂ =10+0.9?, where ?y represents the final exam score and ?x is the midterm exam score. Suppose Joe scores an 80 on the midterm exam. What would be the predicted value of his score on the final exam?
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?
Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ?X is the age of the crab in months and ?ˆY^ is the predicted value of ?Y, the size of the male crab in cm. ?ˆ=9.5603+0.3976?Y^=9.5603+0.3976X What is the value of ?ˆY^ when a male crab is 24.9118 months old? Provide your answer with precision to two decimal places. Y=
Consider the linear regression model ??=?0+?1??+?? and assume that ?(??|??)=4 for each ?=1,...,?. Which one of the following is true about the interpretation of ?0? a. ?0=?(??|??=0) b. ?0 is the estimated average change in the value of ?? when we change the value of ?? c. ?0 is the predicted value of ?? when ??=0 d. ?0=?(??|??=0)−4
Which of the multivariate regression parameters listed below would be best interpreted as: the predicted change in the dependent variable for a one-unit change in an independent variable, holding constant all the other independent variables in the model. a b1 X1 R2
Consider the following hypothetical regression, with FAIL? as a dummy variable for if a business failed in its first year (1=failed, 0=didn’t fail); LOAN is how much money, in thousands of dollars, the business got as a loan when it started; GIG? is a dummy variable for if there was a gig economy job available, such as driving for Lyft (1=available, 0=not available), and COMP is the number of existing competitors the business faced when it started. All variables are statistically significant. FAIL? = 0.63 – 0.01*LOAN – 0.08*GIG? + 0.05*COMP Answer the following: Determine the predicted value of FAIL? if the business had a $30,000 loan, there was no gig economy, and four competitors. In everyday language, what does the estimated value found in A mean? If a business gets an additional six thousand dollars in loans, how would FAIL? change? Give the “punchline” interpretation of the COMP variable: “For every additional competitor…”