Consider the linear model y =B,+B,x+B,x,+B*3,+B,*+u; You estimate the model y =,+B,x+Bx,+u,observations and obtain the OLS residuals You then estimate the auxiliary regression i =Y,+Y,x+Y,x2,+Y*3+Yq*4+based on 1231 li3 3iThe LM statistic3* 3i+v .i11you obtain to test the null hypothesis that HB,=B,=0 is 20.91. What is the R2 of the auxiliary regression?It is not possible to sayO 0.170.175714O 0.177203

Given Number of observations is 123. The LM Statistic to test the null hypothesis that H0 : β2=β4=0…

Answered: Consider the linear model y =ß,+B,x,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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FRQ 2 Professional basketball teams have 11 players per team. Salary is dependent upon their scoring average, measured in points per game. A least-squares regression line that describes the relationship between scoring average and salary for one professional basketball team is ŷ = 2,671,134.68 +684,663.08x, where x is the player's scoring average and y is the player's salary. The residuals for this regression are given in the graph below. Residual $20,000,000 $15,000,000 $10,000,000 $5,000,000 $0 -$5,000,000 -$10,000,000 -$15,000,000 4 ITS % 6 MacBook Pro ● 8 ● ● ● 10 12 14 Scoring Average (Points per Game) Is a line an appropriate model to use for these data? What information tells you this? b) What is the value of the slope of the least-squares regression line? Interpret the slope in the context of this problem. c) What is the predicted salary of the basketball player with 10.9 points per game? d) Approximate the actual salary of the basketball player with 10.9 points per game. 16 tv…
when a regression is used as a method of predicting dependent variables from one or more independent variables. How are the independent variables different from each other yet related to the dependent variable?
Suppose that I want to estimate the effect of x₁ on y. Consider the univariate regression line: how to calculate a and b₁ using OLS? y = a + b₁x₁
An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.
The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r= - 0.972. The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y= - 0.0070x + 44.4405. Complete parts (a) and (b) below. Click the icon to view the data table. ..... (a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per gallon? The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is %. (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. % of the variance in is by the linear model. Data Table (Round to one decimal p Full data set gas mileage Miles per Weight (pounds), x Weight (pounds), x Miles per Gallon, y Car Car Gallon, y…
Let yit denote the outcome of a random variable for the i-th individual at time and let Xit denote a covariate measure on the i-th individual at time t, t, i = 1, ..., n, t = 1,..., T. The data could be modeled using the simple linear regression model: Yit = Bo + B₁xt + Eit, Eit~N(0, t) a) Explain why using this approach may be inappropriate. b) Write a mathematical expression of the random intercept model and the random coefficients models as alternatives to this model. c) Provide an expression for the proportion of variance attributable to each of the variance components in the random coefficients models. d) Write out an expression for the likelihood, priors and posterior for the model in part (c) e) Write out a WinBUGS code for this problem.
Draw a scatterplot of the right foot temperature (y) versus the left foot temperature (x). Then draw the least-squares regression line on the graph.
First Paired Data Set 4 6 7 10 13 11 19 | 21 30. Use the First Paired Data Set. Find the equation for the least-squares regression line. A. y 2 0.804x + 3.282 С. у ~ 0.504х + 1.282 В. у 0.904х + 2.282 D. y 2 0.404x + 0.282
The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are displayed in the scatterplot. The equation ŷ = 17.4 + 0.5x is called the least-squares regression line because it is least able to make accurate predictions for the data. makes the strongest association between weight and height. minimizes the sum of the squared distances from the actual y-value to the predicted y-value. maximizes the sum of the squared distances from the actual y-value to the predicted y-value.
Use the following data for parts (a) through (e). x 5 7 3 16 12 9 y 8 9 11 27 15 13 Determine the equation of the least squares regression line to predict y by x. y^ = (value rounded to 4 decimal places ?) + (value rounded to 4 decimal places ?) x
An engineer is testing a new car model to determine how its fuel efficiency, measured in L/(100 km), is related to its speed, which is measured in km/hour. The engineer calculates the average speed for 30 trials. The average speed is an example of a (statistic or parameter) The engineer would like to find the least squares regression line predicting fuel used (y) from speed (x) for the 30 cars he observed. He collected the data below. Speed 62 65 80 82 85 87 90 96 98 100 Fuel 12 13 14 13 14 14 15 15 16 15 Speed 100 102 104 107 112 114 114 117 121 122 Fuel 16 17 16 17 18 17 18 17 18 19 Speed 124 127 127 130 132 137 138 142 144 150 Fuel 18 19 20 19 21 23 22 23 24 26 The regression line equation is Round each number to four decimal places.
Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 21 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.9, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 10000. From this information, what is the number of degrees of freedom for the t-distribution used to compute critical values for hypothesis tests and confidence intervals for the individual model…

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