Assuming that all LS regression assumptions are valid and only the main effect of x1 and its two-way interactions with the indicator variables are found to be statistically significant: Write down the fitted model for level 1 of the qualitative variable. а. b. Write down the fitted model for level 2 of the qualitative variable. c. Write down the fitted model for level 3 of the qualitative variable.
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- 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 that an interaction term of a dummy variable and a regressor changes the slope of a regression line..The regional transit authority for a major metropolitan area wants to determine whetherthere is a relationship between the age of a bus and the annual maintenance cost. A sampleof ten buses resulted in the following data: a. Develop a scatter chart for these data. What does the scatter chart indicate about therelationship between age of a bus and the annual maintenance cost?b. Use the data to develop an estimated regression equation that could be used to predictthe annual maintenance cost given the age of the bus. What is the estimated regressionmodel?c. Test whether each of the regression parameters b0 and b1 is equal to zero at a 0.05level of significance. What are the correct interpretations of the estimated regressionparameters? Are these interpretations reasonable?d. How much of the variation in the sample values of annual maintenance cost does themodel you estimated in part b explain?e. What do you predict the annual maintenance cost to be for a 3.5-year-old bus?
- The administration of a midwestern university commissioned a salary equity study to help establish benchmarks for faculty salaries. The administration utilized the following regression model for annual salary, y : ?(?) β0+β1x ,where ?=0 if lecturer, 1 if assistant professor, 2 if associate professor, and 3 if full professor. The administration wanted to use the model to compare the mean salaries of professors in the different ranks. a) Explain the flaw in the model. b)Propose an alternative model that will achieve the administration’s objective. c) If the global F-test for the model you proposed in 2 is conducted, what would be the value of the numerator degrees of freedom?A researcher interested in explaining the income levels of St. Lucian workers, developed the following multiple linear regression model: INC = a + BEDU + YEXP+ ST RN where INC = monthly income, EDU = the number of years of formal education, EXP = the number of years of workforce experience and TRN = the number of weeks spent in job training. A sample of 35 workers was processed using MINITAB and the following is an extract of the output obtained: %3D PredictorCoef StDev t-ratio Constant 3315.7 1371.6 2.41 EDU 116.53 26.07 4.47 EXP 282.96 222.8 1.27 TRN -318.12125.74-2.53 S= 2.05 R-sq = 77.3% R-sq(adj) = 75.2% The coefficient y is significant at the 5% level of significance. Select one: O True False3. Wine Participant magazine has collected average price per bottle for the prestigious Chateau Le Thundebird bordeaux for different vintages (years). The data appears in the table below. year of bottling price a) draw the scatter diagram showing how wine price varies by vintage year b) use the most appropriate regression equation to determine the relationship between year of bottling (age) and price. c) what is the explanatory power (RSQ) of that equation d) determine the predicted price of a bottle of this wine for the 2017 vintage. 2009 36 2010 40 2011 51 2012 60 2013 68 2014 72 2015 70 2016 65 2018 51 2019 44 2020 39
- overleaf…/Page 7(b) Finally, the researcher is interested in examining the regression model for knowledge, attitudeand practices towards the COFLU-20. The following model was developed to forecastindividual practices towards COFLU-20 using knowledge and attitude scores.P = α + β K + δ Awhere P = Practice towards COFLU-20 scoreK = Knowledge towards COFLU-20 scoreA = Attitude towards COFLU-20 scoreThe data are processed using MINITAB and the output in Exhibit 1 below was obtained:Exhibit 1The regression equation is *************Predictor Coef SE t-ratio PConstant 4.755 0.462 10.282 0Knowledge 0.8 0.039 2.055 0.041Attitude 0.024 0.6 0.393 0.695R-sq = 81.5%Analysis of VarianceSOURCE DF SS MS F PRegression 2 38.06 19.03 2.284 0.104Error 297 2474.887 8.333Total 299 2512.947(i) Identify the dependent variable(s) and the independent variable(s).[(ii) Is δ significant?Show proof of the testing process used to arrive at your decision.State what this means in terms of attitude and practices.…9) For the same set of observations on a specified dependent variable, two different independent variables were used to develop two separate simple linear regression models. A portion of the results is presented below. R² (R-squared) Model 1 0.92 Based on R2 of each model, which model is more useful? Why? Model 2 0.85The main regression specification of CG involves regressing firm investment rates on market Q, fundamental Q, cash flows, a bubble indicator and an interaction term between bubble and market Q. If you want to see the impact of bubbles on firm investment rates, you will examine significance of Select one: O a. coefficient of the Bubble indicator only O b. sum of the coefficients of market Q and the interaction term. O c. coefficient of the interaction term only O d. sum of the coefficients of Bubble indicator and the interaction term.
- A mail-order business selling personal computer supplies, software and hardware maintains a centralized warehouse. Management is currently examining the process of distribution from the warehouse and wants to study the factors that affect the warehouse distribution costs. Data collected over 24 random months contain the warehouse’s distribution cost (in thousands of Rands), the sales (in thousands of Rands) and the number of orders received. A multiple linear regression model was fitted to the data by using Stat1.2. Use the output to answer the questions that follow by typing only the letter of the correct option in the answer boxes. Variablesy: Warehouse Distribution Costx1: Salesx2: Number of Orders Model Fitting StatisticsR2 = 0.8504Adj R2: ? Regression Coefficients Beta Parameter Standard b Parameter Standard Estimates…Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher’s salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below. (a) What proportion of the variation in MCAS score is explained by the explanatory variables? (b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly. (c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly. (d) Suppose a second regression model (Model 2) was generated using only…Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher’s salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below. (a) What proportion of the variation in MCAS score is explained by the explanatory variables? (b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly. (c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly. (d) Suppose a second regression model (Model 2) was generated using only…
