Derive the least squares estimators (LSEs) of the parameters in the simple linear regression model.
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Derive the least squares estimators (LSEs) of the parameters in the simple linear regression model.
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- In a linear regression model with only one predictor variable, β will equal r. Group of answer choices True FalseThe y-intercept in a linear regression model is always relevant and of interest to investigators for every model constructed. True FalseSuppose that the regression model is defined as: y=B1x+u Use the least squares method to estimate the slope of the regression line. Define the objective function that will be used in the estimation. Lastly, enumerate the steps in deriving the estimator of B1
- 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 study of IT companies has found the following data on the age of each company and its annual volume of sales: Age (years) Sales (000) 2 22 2.5 34 3 33 4 37 4.5 40 4.5 45 5 49 3 30 6 58 6.5 58 (a) Determine the least squares regression that relates the age of company variable to the sales variable in the form y = a + bx. (b) Provide a practical interpretation of the coefficients a and b. (c) Determine the ‘goodness of fit’ (R2) of the estimated regression line. d) Using the estimated regression line determined in (a), calculate what volume of sales would be predicted for a company that is 3.5 years of age. (e) If it was found that…Compute the least-squares regression line for predicting the 2012 budget from the 2006 budget. Round the slope and y- intercept to at least four decimal places.
- Some of the residuals from a least-squares linear model will be positive and some will be negative. TRUE O FALSEA study was conducted to see whether heart rate (y) on swimmers linearly related to their age (x1) and swimming time for 2000 meters (x2). A random sample of ten swimmers was selected and the result is shown in the following Microsoft Excel output. (a)Interpret the value of R2 from the output. (b)Conduct a hypothesis test to test whether the linear regression model is fit or not using a = 0.05. (c)Calculate the 95% confidence interval for the coefficient value for age.An airline developed a regression model to predict revenue from flights that connect "feeder" cities to its hub airport. The response in the model is the revenue generated by flights operating to the feeder cities (in thousands of dollars per month), and the two explanatory variables are the air distance between the hub and feeder city (Distance, in miles) and the population of the feeder city (in thousands). The least squares regression equation based on data for 37 feeder locations last month is Estimated revenue = 81 +0.3Distance + 1.4Population with R² = 0.75 and so = 31.2. Complete parts a through d. (a) The airline plans to expand its operations to add an additional feeder city. The first possible city has population 150,000 and is 275 miles from the hub. A second possible city has population 180,000 and is 250 miles from the hub. Which would you recommend if the airline wants to increase total revenue? The first city The second city
- An oil exploration company wants to develop a statistical model to predict the cost of drilling a new well. One of the many variables thought to be an important predictor of the cost is the number of feet in depth that the must be drilled to create the well. Consequently, the company decided to fit the simple linear regression model, where y = cost of drilling the new well (in $thousands) and x = number of feet drilled to create the well. Using data collected for a sample of n=83 wells, the following results were obtained: = 10.5 + 16.20x Give a practical interpretation of the estimate of the slope of the least squares line. An oil exploration company wants to develop a statistical model to predict the cost of drilling a new well. One of the many variables thought to be an important predictor of the cost is the number of feet in depth that the must be drilled to create the well. Consequently, the company decided to fit the simple linear regression model, where y =…Is the following statement true or false? If false explain briefly. Some of the residuals from a least squares linear model will be positive and some will be negative. (Don't Hand writing in solution)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. 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…
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