Consider a simple linear regression model with one predictor variable X and one response variable Y. The regression equation is given by Y = β0 + β1X, where β0 and β1 are the intercept and slope coefficients, respectively. The sample size is n = 100 and the coefficient of determination (R^2) for the model is 0.25. What can we conclude about the strength of the relationship between X and Y?

In a study, data collected for 40 observations were used to model the dependent variable y with 8 independent variables under consideration, x1, x2, .. , Xg. Consider a stepwise regression run on the data. 1. What is the form of the model fit in step 1? How many models are fit? How is the "best" independent variable selected in this step? 2. What is the form of the model fit in step 2? How many models are fit? How is the "best" independent variable selected in this step? 3. What is the form of the model fit in step 3? How many models are fit? How is the "best" independent variable selected in this step? 4. The variables x3, x4, and x6 were deemed the best variables for predicting y. How do you recommend the researchers proceed from here? Why?

A researcher has developed a regression model from fourteen pairs of data points. He wants to test to determine if the slope is significantly different from zero. He uses a two-tailed test and a = 0.01. The critical tablet value is 2.718 3.012 2.650 O 3.055 O 2.168

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 Conde Nast Traveler Gold List  for 2012 provided rating for the top 20 small cruise ships. The data from annual Readers’ Choice Survey are the overall scores(Y) each ship received based on several criteria, including Itineraries/Schedule (X1), Shore Excursions(X2), and   Food/Dinning(X3). The estimated regression equation to predict the overall scores is Y= 35.6184+0.1105 X1+0.2445 X2+0.2474 X3. Part of the regression results is shown below.                                                            Coefficients       Standard Error Intercept                                           35.6184            13.2308 Itineraries/Schedule(X1)                0.1105               0.1297 Shore Excursions(X2)                      0.2445               0.0434 Food/Dinning(X3)                            0.2474               0.0621     Use the T test to determine whether or not the coefficient of X1 is significant. Use Level of significance=.05? Be sure to state null and alternative hypotheses.…

The difference between a regression weight and a beta weight is: A regression weight assumes linearity. A beta weight is for the population while a regression weight is for the sample. A regression weight is less biased. A beta weight is a standardized regression weight.

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…

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 + ε

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…

The​ least-squares regression equation is y=620.6x+16,624 where y is the median income and x is the percentage of 25 years and older with at least a​ bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7004. Predict the median income of a region in which 30​% of adults 25 years and older have at least a​ bachelor's degree.