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 =…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 12CR

See similar textbooks

Similar questions

Suppose the following regression equation was generated from the sample data of 50 cities relating number of cigarette packs sold per 1000 residents in one week to tax in dollars on one pack of cigarettes and if smoking is allowed in bars: PACKS, = 59682.369232-1108.267218TAX + 176.926159BARS; + eį. BARS 1 if city i allows smoking in bars and BARS; = 0 if city i does not allow smoking in bars. This equation has an R² value of 0.347972, and the coefficient of BARS, has a P-value of 0.133971. Which of the following conclusions is valid? Answer 2 Points Keypad Keyboard Shortcuts According to the regression equation, cities that allow smoking in bars have lower cigarette sales than cities that do not allow smoking in bars. Regardless of whether or not there is a smoking ban, if a city increases its cigarette tax by one dollar cigarette sales will increase by approximately 1108 packs. ○ If there is no cigarette tax in a city that allows smoking in bars, the approximate number of cigarette…
Suppose that n = 50, i.i.d. observations for (Yi, Xi) yield the followingregression results: Ŷ= 49.2 + 73.9X, SER = 13.4, R2 = 0.78. (23.5) (16.4)Another researcher is interested in the same regression, but makes an errorwhen entering the data into a regression program: The researcher enterseach observation twice, ending up with 100 observations (with observation1 entered twice, observation 2 entered twice and so forth).a. Using these 100 observations, what results will be produced by theregression program? (Hint: Write the “incorrect” values of the samplemeans, variances, and covariances of Y and X as functions of the “correct”values. Use these to determine the regression statistics.) Ŷ = ____ + ____X, SER = ____, R2 = ____. (____) (____)b. Which (if any) of the internal validity conditions are violated?
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)
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.
A statistical program is recommended.A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:y = 0 + 1x + wherey traffic flow in vehicles per hourx = vehicle speed in miles per hour.The following data were collected during rush hour for six highways leading out of the city.Traffic Flow(y)Vehicle Speed(x )1,247351,320401,218301, 327451,341501, 11325(a) Develop an estimated regression equation for the data. (Round bo to one decimal place and b1 to two decimal places.) =
The following estimated regression equation based on 10 observations was presented. ŷ = 28.1270 + 0.6906x, + 0.3980x2 (a) Develop a point estimate of the mean value of y when x, = 170 and x2 = 350. (b) Develop a point estimate for an individual value of y when X1 = 170 and X2 = 350.
The following estimated regression equation is based on 10 observations was presented. ŷ 29.1270 +0.59061 +0.498022 Here SST 6,885.875, SSR = 6,231.500, sb = = 0.0728, and 8 = 0.0540. 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 - V c. Perform a t test for the significance of B₁ (to 2 decimals). Use a = 0.05. Use the t table. to = The p-value is -Select your answer - At a= 0.05, there is - Select your answer-relationship between y and ₁. d. Perform a t test for the significance of B₂ (to 2 decimals). Use a = 0.05. Use the t table. to₂ = The p-value is - Select your answer - At a = 0.05, there is Select your answer-relationship between y and #₂.
A simple linear regression was performed on 25 observations. The least squares calculations are given as: SSxy = 204, SSxx= 100, SSyy = 516. Calculate SSE. O 99.84 O 4.34 O 516 O 2.04
The least-square regression line for the given data is y=-0.206x + 2.097. Determine the residual of a data point for which x= 1 and y=-3, rounding to three decimal places. X -5 y 11 OA. - 4.891 OB. - 1.715 O C. - 1.109 OD. 1.891 - 3 -6 4 8 1 - 3 - 1 -2 -2 1 ло 0 5 25 -5 3 6 -40 7
The following estimated regression equation is based on 10 observations was presented. ŷ = 29.1270 + 0.5906x1 + 0.4980x2 . Here SST=6,724.125 , SSR = 6,216.375 , sb1 = 0.0813, sb2 = 0.0567. Compute MSR & MSE to 3 decimals, then compute F using the appropriate F test (round answer to 3 decimals). Use α = 0.05.

SEE MORE QUESTIONS

Recommended textbooks for you

Big Ideas Math A Bridge To Success Algebra 1: Stu…

Algebra

ISBN:

9781680331141

Author:

HOUGHTON MIFFLIN HARCOURT

Publisher:

Houghton Mifflin Harcourt

Glencoe Algebra 1, Student Edition, 9780079039897…

Algebra

ISBN:

9780079039897

Author:

Carter

Publisher:

McGraw Hill

Big Ideas Math A Bridge To Success Algebra 1: Stu…

Algebra

ISBN:

9781680331141

Author:

HOUGHTON MIFFLIN HARCOURT

Publisher:

Houghton Mifflin Harcourt

Glencoe Algebra 1, Student Edition, 9780079039897…

Algebra

ISBN:

9780079039897

Author:

Carter

Publisher:

McGraw Hill

SEE MORE TEXTBOOKS