For the following multiple linear regression model y = Bo + B1x1 + B2x2 + B3x3 + B4x4 + € Derive the test statistic to test Ho : B1 = B2 B3 = B4
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- A local University conducted a survey of over 2,000 MBA alumni to explore the issue of work-life balance. Each participant received a score ranging from 0 to 100, with lower scores indicating a higher imbalance between work and life. A sample of the data is available below. Let x=average number of hours worked per week and y= work-life balance scale score for each MBA alumnus. Investigate the link between these two variables by conducting a complete simple linear regression analysis of the data. Summarize your findings. Hours WLB Score 50 74.09 45 72.45 50 52.93 55 44.33 50 69.15 60 54.79 55 56.26 60 20.44 55 6-.64 50 69.15 70 29.16 45 72.45 40 33.25 40 32.18 45 45.76 a. What is the test statistic for the hypotheses? t=______ b. What is the p-value for the test statistic? p-value=________ c. What is the value for the coeffiecent of determination r^2? r^2=________A seafood-sales manager collected data on the maximum daily temperature, T, and the daily revenue from salmon sales, R, using sales receipts for 30 days selected at random. Using the data, the manager conducted a regression analysis and found the least-squares regression line to be Rˆ=126+2.37T. A hypothesis test was conducted to investigate whether there is a linear relationship between maximum daily temperature and the daily revenue from salmon sales. The standard error for the slope of the regression line is SEb1=0.65. Assuming the conditions for inference have been met, which of the following is closest to the value of the test statistic for the hypothesis test? t=0.274 A t=0.65 B t=1.54 C t=3.65 D t=193.85 EInterpret the following graphs for multiple linear regression and comment on the validity of model assumptions
- 7) Consider the following Matlab outputs for linear regression. Write the suggested regression equation, comment of the results and the quality of the model (interpret the Matlab output): mdl = Linear regression model: y -1 +x1 Estimated Coefficients: Estimate SE tStat pValue (Intercept) х1 6.9506 2.2358 3.1088 0.0020599 -0.043871 0.077609 -0.56528 0.57231 Number of observations: 300, Error degrees of freedom: 298 Root Mean Squared Error: 19.7 R-squared: 0.00107, Adjusted R-Squared -0.00228 F-statistic vs. constant model: 0.32, p-value = 0.572The y-interept bo of a least-squares regression line has a useful interpretation only if the x-values are either all positive or all negative. Determine if the statement is true or false. Why? If the statement is false, rewrite as a true statement.The least-squares regression equation is y=784.6x+12,431 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7962. In a particular region, 26.5 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $29,889. Is this income higher or lower than what you would expect? Why?
- The marketing manager wants to estimate the effect of the MBA program on Salary controlling for the other factors. Which regression model is the MOST appropriate? Oa. Salary = B_0+B_1 MBA + ε Ob. Salary = 3_0+ B_1 MBA + B_2 Work + e c. Salary = B_0+B_1 MBA+B_2 Work + B_3 Age +8 Od. Salary = B_0+ B_1 MBA + B_2 Work + B_3 Age +B_4 Gender + εSuppose that I want to estimate the effect of x₁ on y. Consider the univariate regression line: how to calculate a and b₁ using OLS? y = a + b₁x₁A local University conducted a survey of over 2,000 MBA alumni to explore the issue of work-life balance. Each participant received a score ranging from 0 to 100, with lower scores indicating a higher imbalance between work and life. A sample of the data is available below. Let x = average number of hours worked per week and y=work-life balance scale score for each MBA alumnus. Investigate the link between these two variables by conducting a complete simple linear regression analysis of the data. Summarize your findings. E Click the icon to view the data. The least squares regression equation is y =+ (Ox. (Round to two decimal places as needed.) Revenue and Message Rate for Recent Movies Check the usefulness of the hypothesized model. What are the hypotheses to test? O A. H Bo =0 against H: Bo #0 Hours WLB Score 50 75.22 B. H: B, #0 against H: B, =0 45 78.45 OC. H B, = 0 against H B, 0 50 49.68 55 40.11 OD. H Bo#0 against H: Bo =0 50 70.41 60 55.91 Determine the estimate of the…
- Suppose the following data were collected from a sample of 1515 CEOs relating annual salary to years of experience and the economic sector their company belongs to. Use statistical software to find the following regression equation: SALARYi=b0+b1EXPERIENCEi+b2SERVICEi+b3INDUSTRIALi+eiSALARY�=�0+�1EXPERIENCE�+�2SERVICE�+�3INDUSTRIAL�+��. Is there enough evidence to support the claim that on average, CEOs in the service sector have lower salaries than CEOs in the financial sector at the 0.010.01 level of significance? If yes, write the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence." Copy Data CEO Salaries Salary Experience Service (1 if service sector, 0 otherwise) Industrial (1 if industrial sector, 0 otherwise) Financial (1 if financial sector, 0 otherwise) 144225144225 1010 11 00 00 187765187765 2020 00 00 11 142500142500 66 11 00 00 169650169650 2828 11 00 00 167250167250 3131 00…Consider the following data,Study Hours (Y): 2, 4 ,6 ,8 ,10 ,13, 7Sleeping Hours (X): 10, 9, 8, 7,6 ,7, 5 i) Calculate and analyze the fitted regression line between the number of study hours and the number of sleeping hours of different intakes of CSE students.ii) Find the coefficient of determination and interpret your data.iii) Predict study hour when he/she sleeps 11 hours.Show calculations or explanation for each question. a) Which of the following techniques is used to predict the value of one variable on thebasis of other variables?a. Correlation analysisb. Coefficient of correlationc. Covarianced. Regression analysis b) In the least squares regression line, y^=3-2x the predicted value of y equals:a. 1.0 when x = −1.0b. 2.0 when x = 1.0c. 2.0 when x = −1.0d. 1.0 when x = 1.0 c) In the simple linear regression model, the y-intercept represents the:a. change in y per unit change in x.b. change in x per unit change in y.c. value of y when x = 0.d. value of x when y = 0.
