Use the following information from a multiple regression analysis.n=15b1=2b2=6Sb1=1.4Sb2=0.5a.Which variable has the largest slope, in units of a t statistic?b.Construct a90%confidence interval estimate of the population slope,β1.c.At the0.10level of significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis of these results, indicate the independent variables to include in this model.

Solution: Given information: n= 15 observation k= 2 independent variables b1= 2b2= 6Sb1= 1.4Sb2= 0.5 a) The variable X2 has the largest slope with tSTAT= 12 tSTAT= b2Sb2tSTAT= 60.5=12 b) The 90% confidence interval estimate of the population slope, β1 is b1±tα/2.n-(k+1)×Sb1At α=0.10tα/2,n-(k+1)=t0.05, 12=1.782 From t table ( 2±1.782×1.4)(2±2.4948)(2-2.4948, 2+2.4948)(-0.4948, 4.4948) The 90% confidence interval estimate of the population slope, β1 is ( -0.4948, 4.4948) c) Test for significance of β1 To test the hypothesis Ho:β1=0 VS Ha:β1≠0 Test statistic tSTAT= b1Sb1tSTAT=21.4tSTAT== 1.4286 Test statistic is 1.4286 To find p value p value = 2*P(t> 1.4286) p value = 0.1786 From Excel The p value for the test is 0.1786 Decision: p value > α=0.10 Fail to reject the null hypothesis Conclusion: There is insufficient evidence to conclude that the variable X1 contribute significant to the model. Test for significance of β2 To test the hypothesis Ho:β2=0 VS Ha:β2≠0 Test statistic tSTAT= b2Sb2tSTAT= 60.5=12 Test statistic is 12 To find p value p value = 2*P(t> 12) p value = 0.0000 From Excel The p value for the test is 0.0000 Decision: p value < α=0.10 Reject the null hypothesis Conclusion: There is sufficient evidence to conclude that the variable X2 contribute significantly to the model. Based on the results of hypothesis testing or test for significance of β1 and β2. The independent variable X2 is included in the model.

Answered: Use the following information from a…

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

Write the formula for the estimated regression line and interpret the slope of the estimated regression line, the intercept of the estimated regression line- Is it meaningful?, and the estimated R2. Based on the fitted regression model, what is the predicted ATST for a child who is 7 years old? What is the correlation between AGE and ATST? Does the residual plot suggest that the fitted regression line is inappropriate for these data? Explain why or why not. Suppose that a new subject is added to the study data and that subject is 12.5 years old with an ATST of 580 minutes. If the regression model were to be refit with this additional data point, would the new slope be greater than or less than -14.041? Justify your response.
Given the partial results from a linear regression model below, a sample size of 504, and ɑ=0.05, What is the F-Statistic for the overall model? Is it statistically significant? What is the R2 for the regression model above?
The ANOVA summary table to the right is for a multiple regression model with six independent variables. Complete parts (a) through (e). Draw a conclusion. Choose the correct answer below. (3) Degrees of Source Freedom Regression Error Total 6 26 32 Sum of Squares 240 190 430 A. There is insufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is less than the critical value. O B. There is sufficient evidence of a significant linear relationship with at least one of the independent variables because the p-value is less than the level of significance. C. There is sufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is greater than the level of significance. D. There is insufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is greater than the critical value.
A vocational counselor uses the number of days without employment to predict her clients' feelings of self efficacy, measured on a scale of 1 to 5, with higher numbers meaning that clients feel more secure in their job related abilities. The slope of the regression line is –1.02. Which statement is the best interpretation for this finding? a. For every 1-point increase in self-efficacy, there is an associated decrease in the number of days of unemployment. b. For every additional day of unemployment, there is an associated decrease in self-efficacy of 1.02 points. c. The least number of days a person can be unemployed and still feel self-efficacious is 3.98 points d. The decrease in self-efficacy of 1.02 points is caused by each additional day of unemployment
b. Use statistical software to replicate the following regression analysis with all the Independent variables. Compute the coefficient of multiple determination. (Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.) The regression equation is Paralegal GPA = -0.411 +1.20 HSGPA + 0.00163 SAT_Verbal - 0.00194 SAT_Math Predictor Constant HSGPA SAT Verbal SAT Math 0.001629 -0.001939 Coefficient SE Coefficient -0.4111 1.2014 t 0.7823 -0.53 р 0.622 0.2955 0.002147 4.07 0.010 0.76 0.482 0.002074 -0.94 0.393 Analysis of Variance SOURCE DF SS Regression 3 4.3595 MS F 1.4532 10.33 р 0.014 Residual Error 5 0.7036 0.1407 Total 8 5.0631 Source DF Seq SS HSGPA 1 4.2061 SAT Verbal 1 0.0303 SAT Math 1 0.1231 Coefficient of multiple determination Conduct a global test of hypothesis from the preceding output. c-1. State the decision rule at the 0.05 level of significance. (Round your answer to 2 decimal places.) Reject H₂ if F> c-2. Compute the value of F. (Round…
The following regression model was fitted to sample data with 12 observations: = 30 +4.50x. What is the residual for an observation (x = 2, y = 40)? 0.50 -1 1 -0.50
A car dealership would like to develop a regression model that would predict the number of cars sold per month by a dealership employee based on theemployee's number of years of sales experience. The accompanying regression output was developed based on a random sample of employees. a. Predict the sales next month for an employee with 2.5 years of experience. The predicted sales is 8.6 cars. b. Compute the coefficient of determination and interpret its meaning. The coefficient of determination is 0.234 Therefore, about _________% of the variation in monthly sales is explained by the years of sales experience. (Type an integer or decimal rounded to one decimal place as needed.)
The statistic used to test whether individual regression coefficients are different from zero in the population is: Select one: a. F O b. b Oc. R2 O d. t Clear my choice
An automobile rental company wants to predict the yearly maintenance expense (Y) for an automobile using the number of miles driven during the year () and the age of the car (, in years) at the beginning of the year. The company has gathered the data on 10 automobiles and run a regression analysis with the results shown below:. Summary measures Multiple R 0.9689 R-Square 0.9387 Adj R-Square 0.9212 StErr of Estimate 72.218 Regression coefficients Coefficient Std Err t-value p-value Constant 33.796 48.181 0.7014 0.5057 Miles Driven 0.0549 0.0191 2.8666 0.0241 Age of car 21.467 20.573 1.0434 0.3314 Use the information above to estimate the annual maintenance expense for a 10 years old car with 60,000 miles.
Consider the following computer output from a multiple regression analysis relating the cost of car insurance to the variables: number of car accidents, driver's credit score, and safety rating of the car. Coefficients Coefficients Standard Error t Stat P-value Intercept 956 97.23 9.832 0.0000 Car Accidents 172.08 18.24 9.434 0.0000 (In last 3 years) Credit Score Safety Rating 105.16 201.03 0.523 0.6030 -207.81 20.46 - 10.157 0.0000 Does the sign of the coefficient for the variable credit score make sense? Answer No, because it is expected that as the credit score increases then the cost should decrease. ○ No, because it is expected that as the credit score increases then the cost should also increase. ○ Yes, because it is expected that as the credit score increases then the cost should decrease. ○ Yes, because it is expected that as the credit score increases then the cost should also increase. Tables Keypad Keyboard Shortcuts
Given the correlation coefficient 0.794 and the linear regression equation ŷ = 16.4 +1.58x, compute the coefficient of determination. p² Round to 4 decimal places. =

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

a.	Which variable has the largest slope, in units of a t statistic?
b.	Construct a 90% confidence interval estimate of the population slope, β1.
c.	At the 0.10 level of significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis of these results, indicate the independent variables to include in this model.