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- Write down the null and the alternative hypothesis to test the absence of first order autocorrelation assumption of the classical linear regression modelA marketing professor at Givens College is interested in the relationship between hoursspent studying and total points earned in a course. Data collected on 156 students whotook the course last semester are provided in the file MktHrsPts.a. Develop a scatter chart for these data. What does the scatter chart indicate about therelationship between total points earned and hours spent studying?b. Develop an estimated regression equation showing how total points earned is relatedto hours spent studying. What is the estimated regression model?c. Test whether each of the regression parameters b0 and b1 is equal to zero at a 0.01level 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 total point earned does the modelyou estimated in part b explain?e. Mark Sweeney spent 95 hours studying. Use the regression model you estimated inpart b to predict the total points…True or false: “If the errors in a regression model contain ARCH, they must be serially correlated.”
- Define Least Squares Regression Unbiased Estimators α^, β^, σ^²?A box office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross (in millions of dollars) are collected and stored in the accompanying table. Assuming a linear relationship, use the least-squares method to determine the regression coefficients b0 and b1. Interpret the meaning of the slope, b1, in this problem. Predict the mean opening weekend box office gross for a movie that had 80 million online trailer views. What insights can be obtained about predicting opening weekend box office gross from online trailer views?A study was done to determine whether or not social exclusion causes “real pain.” Researchers looked at a random sample of 7 individuals and measured brain activity in an area of the brain that responds to physical pain to see if activity increases as distress from social exclusion increases (measured by social distress score). The social distress scores in the experiment ranged from 0 to 10. A scatterplot shows a moderately strong linear relationship. The least squares regression line is has a slope of 0.06078 and an intercept of -0.1261. A person has a social distress score of 2.0 and a brain activity level of 0.15. What is their residual?
- A corporation administers an aptitude test to all new sales representatives.Management is interested in the extent to which this test is able to predicttheireventual success. The accompanying table records average weekly sales(inthousands of pesos) and aptitude test scores for a random sample ofeightrepresentatives.1.Plot a scatter diagram2. Estimate the linear regression of weekly sales on aptitude test scores. 3. Estimatethe weekly sales when test scores is 70 4. Determine the coefficient ofdetermination.A Ross MAP team is currently developing a regression model to explain the travel expense of HR consulting firms in a month (measured in thousands of dollars). So far, the team has identified the number of consultants, the number of clients, the number of air-travel trips, and the number of trips to high-expense cities (e.g., NYC, Boston, San Jose) as potential independent variables. A partial output of the corresponding regression model is in Figure 1. Use the figure to answer question 4to6 4. What is the R2 and adjusted R2 of the model? 5. What is the standard error of the estimates (serror) in thousands of dollars? 6. Based on what you can learn from this table, what is your assessment about the model? For your information, the firm with the lowest travel expense was $47K and the firm with the highest expense was $125K in the sample data.An agronomist undertook an experiment to investigate the factors that potato harvest. In his research, agronomist decided to divide the farm into 30 half hectare plots and apply varies level of fertilizer. Potato was then planted and the harvest at the end of the season was recorded. Fertilizer(Kg) Harvest (tons) 210 43.5 220 40.0 230 48.0 240 65.0 250 80.0 260 85.0 270 95.0 280 80.0 290 97.3 1. Find the simple regression line and interpret the coefficients. 2. Find the coefficient of determination and interpret its value. 3. Does the model appear to be a useful tool in predicting the potato harvest? If so, predict the harvest when 250KG of fertilizer is applied. If not explain why not.
- Define the Linear Regression Model. Also explain Terminology for the Linear Regression Model with a Single Regressor?A local government conducted a study to investigate the relationship between the number of unauthorized days employees are absent per year and the distance(miles) between home and work for employees. The table below gives the results for ten employees. Distance to work (miles) Number Days Absent 1 8 3 5 4 8 6 7 8 6 10 3 12 5 14 2 14 4 18 2 Sketch a scatter diagram for the data. Is a linear relationship reasonable? Explain. Develop the least squares estimate regression equation that relates the distance to work to the number of days absent. Predict the number of days absent for an employee that lives 5 miles from work.Carbon dioxide (CO,) is produced by burning fossil fuels such as oll and natural gas, and has been connected to global warming. The following table presents the average amounts (in metric tons) of COy emissions for certain years per person in the United States and per person in the rest of the world. Use a TI-84 calculator to answer the following, (a) Compute the least-squares regression line for predicting U.S. emissions from non-U.S. emissions. Round the slope and y-intercept values to four decimal places.