**Multiple Choice**- O Reject the null hypothesis that \( \beta_3 = 0 \).- O Reject the null hypothesis that \( \beta_1 = 0 \).- O Reject the null hypothesis that \( \beta_1 = \beta_2 = \beta_3 = \beta_4 = 0 \).- O Do not reject the null hypothesis that \( \beta_1 = \beta_2 = \beta_3 = \beta_4 = 0 \). **Multiple Regression Model Analysis**Consider the multiple regression model presented here, involving the dependent variable \( Y \) and four independent variables \( X_1, X_2, X_3, \) and \( X_4 \). The resulting function is as follows:\[\hat{Y} = 33 + 8X_1 - 6X_2 + 16X_3 + 18X_4\]For this model, 35 observations were recorded. The sum of squares for regression (SSR) is 1,432, while the sum of squares for error (SSE) is 600. The analysis assumes a significance level of 0.01.Based on the provided information, which of the following conclusions is correct regarding the statistical significance of the overall model?

Solution: Given information: n= 35 observation k = 4 independent variables Sum of square of…

Answered: Consider the multiple regression model…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

You may need to use the appropriate technology to answer this question. A regression analysis involving 45 observations relating a dependent variable and two independent variables resulted in the following information. ŷ = 0.406 + 1.3385x₁ + 2x₂ The SSE for the above model is 43. When two other independent variables were added to the model, the following information was provided. ŷ = 1.9 - 3x₁ + 12x2 + 4x3 + 8x4 This model's SSE is 36. At a 0.05 level of significance, test to determine if the two added independent variables contribute significantly to the model. State the relevant null and alternative hypotheses. O Ho: One or more of the parameters is not equal to zero. H₂: B₁ = P₂ = P3 =B4 = 0 B1 O Ho: One or more of the parameters is not equal to zero. H₂: B3 =B₁ = 0 O Ho: B3 = P4 = 0 H₂: None of the parameters are equal to zero. O Ho: B3 B4= = = H₂: One or more of the parameters is not equal to zero. O Ho: P₁ = P₂ = P3= P4= H: One or more of the parameters is not equal to zero. Find…
The datasetBody.xlsgives the percent of weight made up of body fat for 100 men as well as other variables such as Age, Weight (lb), Height (in), and circumference (cm) measurements for the Neck, Chest, Abdomen, Ankle, Biceps, and Wrist. We are interested in predicting body fat based on abdomen circumference. Find the equation of the regression line relating to body fat and abdomen circumference. Make a scatter-plot with a regression line. What body fat percent does the line predict for a person with an abdomen circumference of 110 cm? One of the men in the study had an abdomen circumference of 92.4 cm and a body fat of 22.5 percent. Find the residual that corresponds to this observation. Bodyfat Abdomen 32.3 115.6 22.5 92.4 22 86 12.3 85.2 20.5 95.6 22.6 100 28.7 103.1 21.3 89.6 29.9 110.3 21.3 100.5 29.9 100.5 20.4 98.9 16.9 90.3 14.7 83.3 10.8 73.7 26.7 94.9 11.3 86.7 18.1 87.5 8.8 82.8 11.8 83.3 11 83.6 14.9 87 31.9 108.5 17.3…
The U.S. Department of Energy’s Fuel Economy Guide provides fuel efficiency data for cars and trucks. The following regression output was obtained for a sample of 45 cars. The variable of interest is highway miles per gallon (Hwy MPG). The independent variables used in the analysis are as follows: The class of the vehicle: Compact, Midsize or Large. Midsize = 1 if the car is a midsize, 0 otherwise. Similarly, Large = 1 if it is a large car, 0 otherwise. Displcement: The engine displacement (size) in liters Premium: Equals 1 if premium fuel is used, 0 if regular fuel is used Cylinders: Number of cylinders Regression Statistics Multiple R 0.90 R Square Adjusted R Square 0.79 Standard Error 1.78 Observations 45 ANOVA df SS MS F Significance F…
need help. please
I need help answering this question.
Using 23 observations on each variable, a computer program generated the following multiple regression model. y = 65.5 +9.56x1+3.27x2-4.23x3– 9.23x4 If the standard errors of the coefficients of the independent variables are, respectively, 3.44, 2.30, 2.76, and 4.99, can you conclude that the independent variable x, is needed in the regression model? Let B1, B2, Ba denote the coefficients of the 4 variables in this model, and use a two-sided hypothesis test and significance level of 0.10 to determine your 4 .../ answer. (a) State the null hypothesis H, and the alternative hypothesis H,. H, : 0 H, : 0 (b) Determine the type of test statistic to use. Degrees of freedom: D=0 OSO (c) Find the value of the test statistic. (Round to two or more decimal places.) O#0 OO (d) Find the two critical values at the 0.10 level of significance. (Round to two or more decimal places.) | and || (e) Can you conclude that the independent variable is needed in the regression model? Yes No 미
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
Body Fat. Where we considered the regression of percentage of body fat on nine body measurements: height, weight, hip, forearm, neck, wrist, triceps, scapula, and sup. Use the technology of your choice to do the following. a. Use the maximum- R2 criterion to obtain a regression equation for these data. b. Use the adjusted- R2 criterion to obtain a regression equation for these data. c. Use the Mallows’ Cp criterion to obtain a regression equation for these data. d. Are the regression equations obtained in parts (a), (b), and (c) the same? e. Use the analysis in parts (a), (b), and (c) to select a regression equation for these data. For the regression equation that you selected, obtain plots of residuals versus fitted values, residuals versus the included predictor variables, and a normal probability plot of the residuals. Perform a residual analysis to assess the appropriateness of the regression equation, constancy of the conditional standard deviations, and normality of the…
Let sale denote the sale price for a house, sqft its square footage, and days the number of days that it has been on the market. Consider running two different regressions: First regression: sale = B1 + B2sqft + ß3days + e Second regression: sale = Bi + B2sqft + e Which of the following statements is false? In the options below, the quantities SST, SSE, and SSR are as defined when we discussed R?, that is SST = E(Y, – Ỹ)², SSE = E(Y; - Ý )², and SSR = i=1 O a. The SST from the first regression can be strictly smaller than the SST from the second regression. O b. The SSE from the first regression can be strictly smaller than the SSE from the second regression. O c. The R- from the first regression can be strictly larger than the R2 from the second regression. O d. The R2 from the second regression is equal to the R2 from the regression sqft = Yi + Y2sale + e O e. The SSR from the first regression can be strictly larger than the SSR from the second regression.
You are given the following data, where X1X1 (final percentage in science class) and X2X2 (number of absences) are used to predict YY (standardized science test score in third grade): X1X1 X2X2 YY 95 2 415 82 0 400 92 6 375 72 1 410 75 4 370 80 1 390 78 3 350 70 3 345 65 7 300 70 3 350 88 3 375 89 1 450 Determine the following multiple regression values.Report intercept and slopes for regression equation accurate to at least 2 decimal places: Intercept: b0=b0= Partial slope X1X1: b1=b1= Partial slope X2X2: b2=b2= Report the coefficient of multiple determination for the model (NOT the adjusted R2R2) and the sum of squares total accurate to at least 2 decimal places: R2=R2= SSTotal=SSTotal= Test the significance of the overall regression model. F-test statistic = P-value = Report the Mean Squares residuals accurate to 2 decimal places: Report the test statistics for the regression coefficients accurate to 2 decimal places:…
Use the following table and information to answer questions 21 and 22: A company wants to build anew site with the number of bathrooms commensurate with the number of employees who will workthere. The analytics team decides to analyze a linear model of these data from extant sites to inform thisdecision before construction. Number of employees 650 730 810 900 102 107 1150 Number of bathrooms 40 50 54 61 82 110 121 21. The linear regression equation is:a. y-hat = 79.96 + 0.0094xb. y-hat = 0.0094 – 79.96xc. y-hat = 0.0094 – 79.96xd. y-hat = 79.96 – 0.0094x22. Predict how many bathrooms a new site with 1150 employees should have.a. 91b. 70c. 121d. The linear regression equation should not be used to make predictions.

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS