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- What do we mean when we say that a multiple regression model is a multiple linear regression model? What does “linear” mean here? Can we allow any “higher-order terms”? Explain.| Draw a scatter plot of Y versus X for a simple linear regression analysis where case 1 has a large studentized residual but small leverage, and case 2 has a small studentized residual but high leverage (hat value). Please label the points clearly. You can draw the plot by hand or using R by generating your own data.The experimenters conducted a regression analysis on the results and made the output from the analysis publicly available on Open Science Framework (osfio/fm5c2). From this output, we can derive that regression equation shown here. The equation predicts participants' relative performance estimates (from 0% to 99%) from their scores on the measure of their theories of intelligence, while controlling their actual scores on the antoymns test. Remember: The theories of intelligence survey includes a series of statements that participants rate on a scale of 1 to 6; average scores on the overall measure range from 1, indicating views of intelligence as highly stable; to 6, indicating views of intelligence as highly changeable. Relative performance estimate = 12.10 (theories of intelligence score) +0.13 (antonyms test score). Based on this regression equation, what kind of regression analysis did the researchers perform? a. A simple linear regression analysis b. Multiple regression analysis…
- 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=________If I want to estimate the regression of a model by using OLS on Eveiws , and I chose the "keep it as general as possible" approach, what tests can I apply through the estimation and inference process to validate the model and the variables?Hormone replacement therapy (HRT) is thought to increase the risk of breast cancer. The accompanying data on x = percent of women using HRT and y = breast cancer incidence (cases per 100,000 women) for a region in Germany for 5 years appeared in the paper "Decline in Breast Cancer Incidence after Decrease in Utilization of Hormone Replacement Therapy." The authors of the paper used a simple linear regression model to describe the relationship between HRT use and breast cancer incidence. t HRT Use Breast Cancer Incidence 46.30 40.60 39.50 36.60 30.00 103.30 105.00 100.00 93.80 83.50 (a) What is the equation of the estimated regression line? (Round your numerical values to four decimal places.) ŷ = (b) What is the estimated average change in breast cancer incidence (in cases per 100,000 women) associated with a 1 percentage point increase in HRT use? (Round your answer to four decimal places.) cases per 100,000 women (c) What breast cancer incidence (in cases per 100,000 women) would be…
- Show the best fitted line on scatter diagram and Find the predicted value for each y using the exposure time and the equation obtained in part b (b. Find the equation of regression line between radiation doses on exposure time .usingleast square method)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 + εFor a linear regression problem, The actual observed y-value when x = 2 is y = 6. The least squares line is y = 2x+1. The predicted value when x=2 is y = 5. Determine the value of the residual (prediction error) oooo 1 6 5 Cannot be determined from the information given
- A retail company wants to understand the factors that impact its sales revenue. The company has collected data on the following variables for the past 5 months: Total sales revenue (Y), Average store foot traffic (XI), and Marketing budget (X3). Develop a multiple linear regression model to predict that, what is the impact of average store foot traffic, and marketing budget on total sales revenue for the retail company. The data is summarized in Table 4. Table 4 Average Store foot traffic (X1) Sales Revenue (Y) 50$ 5 130S 45$ 48$ 7 6 120$ 200$ 60$ 708 5 4 Marketing Budget (X2) 130$ 250$ Note: Average Store foot traffic is the average number of people enter in the store per minuteA 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…