Given the linear regression model:Yi = Bo+B1x1 + ẞ2xi2 + Єi,i = 1,..., nConsider the following sums from n = 10 observations on Y, X1, and X2:101010Σ3 = 20, Σi=110Συ? = 98.2,i=1i=110101071 =0.0, Σi=110x12 = 0.0Σαμ = 92, Σα?i=1= 163i=110Σ Yixil=59, Yixi2 = 88,Xi1i2=119i=1i=1i=1Explore the following steps:1. Construct the XTX matrix and the vector XTy.2. Calculate the least-squares estimates of Bo, B₁, and ẞ2, along with the residual sum ofsquares, SSE.3. Investigate the hypothesis that the coefficient of X 2, represented by 32, is zero.

Question: 1) First, let's construct the X^T X matrix and X^T y vector. For X^T X: - The design…

Answered: Given the linear regression model: Yi =…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

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A regression was run to determine if there is a relationship between hours of TV watched per day (xx) and number of situps a person can do (yy).The results of the regression were:y=ax+b a=-0.853 b=34.041 r2=0.389376 r=-0.624 Use this to predict the number of situps a person who watches 7 hour(s) of TV can do, and please round your answer to a whole number.
Find out the regression coefficients of Y on X and X on Y from the following data: Σ Χ= 50 , X-5, Σ Y= 60, Y-6, ΣΧΥ- 350. Variance of X= 4, Variance of Y = 9.
For each gender, estimate an earnings regression where the dependent variable is Annual Earnings and the independent variable is Age. Report the results for each regression, and provide an interpretation of the coefficient associated with age. Female- annual earning: 49347.58 age: 42.81 education: 14.4 Male- Annual earning: 69984.54 age: 42.86 education: 14.11.
Q22. Find out the regression coefficients of Y on X and of X on Y on the basis of following data: ΣΧ- 50 X = 5, Er = 60, F=6, ΣΧΥ-350 Variance of X= 4, Variance of Y= 9
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).The results of the regression were:y=ax+b a=-1.38 b=39.555 r2=0.693889 r=-0.833 Assume the correlation is significant, and use this to predict the number of situps a person who watches 7 hours of TV can do (to one decimal place)
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The following estimated regression equation is based on 10 observations was presented. ŷ = 29.1270 + 0.5906x1 + 0.4980x2 Here SST = 6,871.500, SSR = 6,526.625 , si, = 0.0762, and Si, = 0.0612. a. Compute MSR and MSE (to 3 decimals). MSR MSE = b. Compute F and perform the appropriate F test (to 2 decimals). Use a = 0.05. Use the F table. F The p-value is between 0.025 and 0.05 At a = 0.05, the overall model is not significant c. Perform at test for the significance of B1 (to 2 decimals). Use a = 0.05. Use the t table. The p-value is between 0.02 and 0.05 v At a = 0.05, there is not a significant relationship between y and 01. d. Perform a t test for the significance of B2 (to 2 decimals). Use a = 0.05. Use the t table. The p-value is between 0.01 and 0.02 v At a = 0.05, there is not a significant v relationship between y and x2.
Consider a simple linear regression model Yi = Bo + B1xi + Ei, i= 1,2, 3 with x; = i/3 for i = 1, 2, 3. Assume that %3| E1 1 -1 0 E = E2 ~ N -1 E3. 3 What is the smallest variance for an unbiased estimate of B1?
The following estimated regression equation is based on 10 observations was presented. ŷ = 29.1270 + 0.590601 + 0.4980x2 Here SST = 6,898.250, SSR = 6,009.500, S, = 0.0712, and S, = 0.0566. a. Compute MSR and MSE (to 3 decimals). MSR MSE b. Compute F and perform the appropriate F test (to 2 decimals). Use a = 0.05. Use the F table. F= The p-value is Select your answer - At a = 0.05, the overall model is -Select your answer - c. Perform a t test for the significance of 61 (to 2 decimals). Use a = 0.05. Use the t table. The p-value is Select your answer - At a = 0.05, there is - Select your answer- v relationship between y and a1. d. Perform a t test for the significance of 82 (to 2 decimals). Use a = 0.05. Use the t table. The p-value is Select your answer - At a = 0.05, there is - Select your answer - v relationship between y and 2.
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