The linear regression results below are based on commercial properties that real estate agencies use to guide clients with quantitative information helpful to make rental decisions. A random sample of 27 properties are considered with data for the variables, age of the property (X1), operating expenses and taxes (X2), vacancy rates (X3), total square footage (X4), and rental rates (Y). Parameter Estimator

The linear regression results below are based on commercial properties that real estate agencies use to guide clients with quantitative information helpful to make rental decisions. A random sample of 27 properties are considered with data for the variables, age of the property (X1), operating expenses and taxes (X2), vacancy rates (X3), total square footage (X4), and rental rates (Y). Parameter Estimator

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 76E

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If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?
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The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature (x1), the number of days in the month (x2). The past year’s historical data are available and are presented in the following table: Fit a multiple linear regression model to these data.
The measure of standard error can also be applied to the parameter estimates resulting from linear regressions. For example, consider the following linear regression equation that describes the relationship between education and wage: WAGEi=β0+β1EDUCi+εi where WAGEi is the hourly wage of person i (i.e., any specific person) and EDUCi is the number of years of education for that same person. The residual εi encompasses other factors that influence wage, and is assumed to be uncorrelated with education and have a mean of zero. Suppose that after collecting a cross-sectional data set, you run an OLS regression to obtain the following parameter estimates: WAGEi=−11.5+6.1 EDUCi If the standard error of the estimate of β1 is 1.32, then the true value of β1 lies between(4.78, 4.12, 3.46, 5.44) and (6.76, 7.42, 8.74) . As the number of observations in a data set grows, you would expect this range to (DECREASE , INCREASE) in size.
A simple linear regression model was created to examine the relationship between the age of patients in years (i.e. the independent variable) and the patients' scores on a questionnaire that measures quality of life (i.e. the dependent variable). There were n=20 patients in the study, and some of the results of the regression are presented below: Estimated slope = -0.64 Standard error of the slope = 0.52 Estimated intercept = 42.0 Standard error of the intercept = 13.6 Based on these results, what would be the expected quality of life score for a patient who is 30 years old? Question 3 options: 61.2 22.8 1260.64 29.2
A simple linear regression model was created to examine the relationship between the age of patients (i.e. the independent variable) and the patients' scores on a questionnaire that measures quality of life (i.e. the dependent variable). There were n=20 patients in the study, and some of the results of the regression are presented below: Estimated intercept = 42 Standard error of the intercept = 13.6 Estimated slope = -0.64 Standard error of the slope = 0.52 Based on these results, which of the following can we conclude, based on an alpha level of 0.05 for significance? Question 16 options: The intercept is not significantly different from 0, but the slope is significantly different than 0. Thus, we have mixed results and we cannot make a definitive statement about the significance of the association. There is a significant association, because the intercept is statistically significantly different than 0 (p<0.05). There is not a…
Compute for the necessary linear regressions based on the given data. (can use Excel or Minitab for this) The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in degF) for that month. The past year’s usage and temperature are shown in the following table: (a) Assuming that a simple linear regression model is appropriate, fit the regression model relating steam usage (y) to the average temperature (x).(b) What is the estimate of expected steam usage when the average temperature is 55F?
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 73.22 45 70.79 50 48.78 55 44.15 55 69.89 60 53.15 50 56.04 60 22.53 50 60.73 55 69.89 70 29.17 45 70.79 40 33.38 40 32.13 45 46.17 The least squares regression equation is y=enter your response here+enter your…
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 73.22 45 70.79 50 48.78 55 44.15 55 69.89 60 53.15 50 56.04 60 22.53 50 60.73 55 69.89 70 29.17 45 70.79 40 33.38 40 32.13 45 46.17 Check the usefulness of the hypothesized model. What are the hypotheses to test?…
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=________
The quality of the orange juice produced by a certain manufacturer is constantly monitored. Data collected on the sweetness index of an orange juice sample and amount of water-soluble pectin for 24 production runs at a juice manufacturing plant are shown in the accompanying table. Suppose a manufacturer wants to use simple linear regression to predict the sweetness (y) from the amount of pectin (x). Find and interpret the coefficient of determination, r2, and the coefficient of correlation, r. Find and interpret the coefficient of determination, r2. Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) A. The coefficient of determination, r2, is enter your response here. Sample variations in the amount of water-soluble pectin explain 100r2% of the sample variation in the sweetness index using the least squares line. B. The coefficient of determination, r2, is enter your…