Suppose the simple linear regression model, Y; = Bo + B1 x; + E;, is used to explain the relationship between x and y. A random sample of n = 10 values for the explanatory variable (x) was selected and the corresponding values of the response variable (y) were observed. The summary statistics were: Σο-8, Συ- 10, Σ-9.5, Σ-7.4,Συ?- 20

Suppose the simple linear regression model, Y; = Bo + B1 x; + E;, is used to explain the relationship between x and y. A random sample of n = 10 values for the explanatory variable (x) was selected and the corresponding values of the response variable (y) were observed. The summary statistics were: Σο-8, Συ- 10, Σ-9.5, Σ-7.4,Συ?- 20

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.
In an instrumental variable regression model with one regressor, Xi, andone instrument, Zi, the regression of Xi onto Zi has R2 = 0.1 and n = 50.Is Zi a strong instrument? Would your answer change if R2 = 0.1 and n = 150?
In a data set with 12 observations, you try fitting two regression models. The esti-mated models are summarized as: Model 1: Y(hat) =3.5 + 2x; SSR= 5, and SSE= 10;Model 2: Y(hat) =3.0 + 1.5x + 0.4^2; SSR=23, and SSE=7 (a) Calculate R2 for both models. b. for both models test the null hypothesis that all the regression coefficients other than the intercept are 0.
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?
The following estimated regression equation is based on 10 observations y = 30.12 + .60x1 + .48x2 SST = 680.3, SSR= 601.4, Sb1 = .0813 and Sb2 = .0567 a. Compute MSR and MSE b. Compute F and perform the appropriate F test. Use alpha = .05. c. Perform a t test for the significance of B1. Use alpha = .05. d. Perform a t test for the significance of B2. Use alpha = .05.
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 - 0.433x
The following estimated regression equation is based on 10 observations yhat = 30.12 + .60x1 + .48x2 SST = 680.3, SSR= 601.4, Sb1 = .0813 and Sb2 = .0567 a. Compute MSR and MSE b. Compute F and perform the appropriate F test. Use alpha = .05. c. Perform a t test for the significance of B1. Use alpha = .05. d. Perform a t test for the significance of B2. Use alpha = .05.
Q11. A fitted linear regression equation is ŷ = 6–2x. If x = 3 and the corresponding observedvalue of y = 2, the residual at this observation is:a. –5b. 2c. –3d. –2
In a regression analysis involving 27 observations, the following estimated regressionequation was developed:yˆ 5 25.2 1 5.5x1For this estimated regression equation SST = 1550 and SSE = 520.a. At a = .05, test whether x1 is significant.Suppose that variables x2 and x3 are added to the model and the following regressionequation is obtained.yˆ 5 16.3 1 2.3x1 1 12.1x2 2 5.8x3For this estimated regression equation SST = 1550 and SSE = 100.
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