A student at a junior college conducted a survey of 20 randomly selected full-time students to determine the relation between the number of hours of video game playing each week, x, and grade-point average, y. She found that a linear relation exists between the two variables. The least-squares regression line that describes this relation is y = - 0.0506x +2.9361. (a) Predict the grade-point average of a student who plays video games 8 hours per week. The predicted grade-point average is (Round to the nearest hundredth as needed.)
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- A prospective MBA student would like to examine the factors that impact starting salary upon graduation and decides to develop a model that uses program per-year tuition as a predictor of starting salary. Data were collected for 37 full-time MBA programs offered at private universities. The least squares equation was found Y = -13258.594 + 2.422X,, where X; is the program per-year tuition and Y; is the predicted mean starting salary. To perform a residual analysis for these data, the following results are obtained. of regression have been seriously violated. Residual index plot QQ Plot of Residuals Residuals Residuals 20000 20000 -20000 -20000 -40000 40000 TO 20 Index Normal Quantile Residuals vs. Program Per-Year Tuition ($) Residuals Predicted Values vs. Residuals Predicted Values 20000 140000- 120000- 100000 80000- -20000 60000 -40000 40000- 30000 50000 4000 Program Per-Year Tuition ($) 20000 60000 70000 -20000 20000 Residuals ..... a) To evaluate whether the assumption of linearity…The following table shows the length, in centimeters, of the humerus and the total wingspan, in centimeters, of several pterosaurs, which are extinct flying reptiles. (A graphing calculator is recommended.) (a) Find the equation of the least-squares regression line for the data. (Where × is the independent variable.) Round constants to the nearest hundredth. y= ? (b) Use the equation from part (a) to determine, to the nearest centimeter, the projected wingspan of a pterosaur if its humerus is 52 centimeters. ? cmThe least-squares regression equation is y=784.6x+12,431 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 0.7962. In a particular region, 26.5 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $29,889. Is this income higher or lower than what you would expect? Why?
- Suppose a researcher collects data on houses that have been sold in a particular neighbourhood over the past year, and obtains the regressions results in the table shown below. A family purchases a 2000 square foot home and plans to make extensions totalling 500 square feet. The house currently has a pool, and a real estate agent has reported that the house is in excellent condition. However, the house does not have a view, and this will not change as a result of the extensions. According to the results in column (1), what is the expected DOLLAR increase in the price of the home due to the planned extensions?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…An automotive engineer computed a least-squares regression line for predicting the gas mileage (mpg) of a certain vehicle from its speed in mph. The results are presented in the following Excel output: What is the regression equation? Intercept Speed R-Sq Coefficients 40.69 -0.22 0.588. Og = 40.69 0.22X Oy = 40.69 0.588X Oŷ = 0.22 + 40.69X Oy = 0.588 0.22X
- Biologist Theodore Garland, Jr. studied the relationship between running speeds and morphology of 49 species of cursorial mammals (mammals adapted to or specialized for running). One of the relationships he investigated was maximal sprint speed in kilometers per hour and the ratio of metatarsal-to-femur length. A least-squares regression on the data he collected produces the equation ŷ = 37.67 + 33.18x %3D where x is metatarsal-to-femur ratio and ŷ is predicted maximal sprint speed in kilometers per hour. The standard error of the intercept is 5.69 and the standard error of the slope is 7.94. Construct an 80% confidence interval for the slope of the population regression line. Give your answers precise to at least two decimal places. Lower limit: Upper limit:A real estate analyst has developed a multiple regression line, y = 60 + 0.068 x1 – 2.5 x2, to predict y = the market price of a home (in $1,000s), using two independent variables, x1 = the total number of square feet of living space, and x2 = the age of the house in years. With this regression model, the predicted price of a 10-year old home with 2,500 square feet of living area is __________. $205.00 $200,000.00 $205,000.00 $255,000.00We have data from 209 publicly traded companies (circa 2010) indicating sales and compensation information at the firm-level. We are interested in predicting a company's sales based on the CEO's salary. The variable sales; represents firm i's annual sales in millions of dollars. The variable salary; represents the salary of a firm i's CEO in thousands of dollars. We use least-squares to estimate the linear regression sales; = a + ßsalary; + ei and get the following regression results: . regress sales salary Source Model Residual Total sales salary cons SS 337920405 2.3180e+10 2.3518e+10 df 1 207 208 Coef. Std. Err. .9287785 .5346574 5733.917 1002.477 MS 337920405 111980203 113066454 Number of obs F (1, 207) Prob > F R-squared t P>|t| = Adj R-squared = Root MSE 1.74 0.084 5.72 0.000 = = -.1252934 3757.543 = 209 3.02 0.0838 0.0144 0.0096 10582 [95% Conf. Interval] 1.98285 7710.291 This output tells us the regression line equation is sales = 5,733.917 +0.9287785 salary. Interpret 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.A biologist is interested in predicting the percentage increase in lung volume when inhaling (y) for a certain species of bird from the percentage of carbon dioxide in the atmosphere (x). Data collected from a random sample of 20 birds of this species were used to create the least-squares regression equation ŷ = 400-0.08x. Which of the following best describes the meaning of the slope of the least-squares regression line? (A) The percentage increase in lung volume when inhaling increases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (B) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on average, for every 1 percent increase in lung volume when inhaling. (C) The percentage increase in lung volume when inhaling decreases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (D) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on…An advertising firm wishes to demonstrate to potential clients the effectiveness of the advertising campaigns it has conducted. The firm is presenting data from 12 recent campaigns, with the data indicating an increase in sales for an increase in the amount of money spent on advertising. In particular, the least-squares regression equation relating the two variables cost of advertising campaign (denoted by x and written in millions of dollars) and resulting percentage increase in sales (denoted by y) for the 12 campaigns is y = 6.18 +0.14x, and the standard error of the slope of this least-squares regression line is approximately 0.10. Using this information, test for a significant linear relationship between these two variables by doing a hypothesis test regarding the population slope B₁. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.10 level of significance, and perform a two-tailed…