Given X= 4Y + 5 and Y = KX + 4 are the lines of %3D regression of X on Y and Y on X respectively. If K is positive, prove that it cannot exceed 14. If K = 1/16, find the means of two variables and the coefficient of correlation between them.
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- Two variable are found to have a strong negative linear correlation. Pick the regression equation that best fits this scenario. Oŷ = 0.32x 30 Oy = 0.82x - 30 Oy y = -0.32x + 30 -0.82x + 30A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled " The relation of dive duration (DD) to depth (D)." Duration DD is measured in minutes and depth D is in meters. The report then says, " The regression equation for this bird is: DD = 2.02 + 0.0081 D. (a) What is the slope of the regression line?. ANSWER minutes per meter. (b) According to the regression line, how long does a typical dive to a depth of 400 meters last? ANSWER minutes. SpeakThe owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x,) and newspaper advertising (x,). The estimated regression equation was ý = 83.3 + 2.24x, + 1.30x2. The computer solution, based on a sample of eight weeks, provided SST 25.2 and SSR = 23.455. %D (a) Compute and interpret R² and R,. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is . Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (b) When television advertising was the only independent variable, R = 0.653 and R, = 0.595. Do you prefer the multiple regression results? Explain. %3D 2 Multiple regression analysi v ---Select--- ipreferred since both R2 and R, show ---Select--- O…
- Q12) If the slope of the regression equation y=b0+b1×x is equal to negative, then; 1. as x increases y decreases 2.. as x changes, y does not change 3.. Either a or b is correct 4.. as x decreases y increasesSelect the appropriate interpretation for the slope of the linear regression equation below. Y (Dependent Variable) = Grade Point Average X (Independent Variable) = Average number of hours spent using electronic devices for entertainment purposes yhat = 4 - 0.125*X A. For every 1 hour more spent using electronic devices for entertainment per week then a person's GPA will increase on average by 0.125 points B. For every 1 GPA gained obtained by a student then on average that person will have watched 0.125 hours fewer of entertainment on electronic devices per week C. For every 1 GPA point lost by a student then on average that person will have watched 0.125 hours more of entertainment on electronic devices per week D. For every 1 hour more spent using electronic devices for entertainment per week then a person's GPA will decrease on average by 0.125 pointsThe owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x,) and newspaper advertising (x,). The estimated regression equation was ý = 82.3 + 2.29x, + 1.90x2. The computer solution, based on a sample of eight weeks, provided SST = 25.1 and SSR = 23.415. (a) Compute and interpret R? and R 2. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is 653 x . Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (b) When television advertising was the only independent variable, R2 = 0.653 and R,2 = 0.595. Do you prefer the multiple regression results? Explain. Multiple regression analysis (is preferred since both R2 and R.2 show an increased v v…
- Let x be the size of a house (in square feet) and y be the amount of natural gas used (therms) during a specified period. Suppose that for a particular community, x and y are related according to the simple linear regression model with the following values. ? = slope of population regression line = 0.016 ? = y intercept of population regression line = −7 Question: Graph the population regression line by first finding the point on the line corresponding to x = 1,000 and then the point corresponding to x = 2,000, and drawing a line through these points.It is known that the linear regression equation: y= -2.88+1.77x, with a coefficient of determination of 0.81. Based on the two information, the correlation coefficient isTwo lines of regression are 2x - y - 20 = 0, 2y - x + 4 = 0. The correlation coefficient is
- 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 $255,000.00A study tests the effect of earning a Master's degree on the salaries of professionals. Suppose that the salaries of the professionals (S,) are not dependent on any other variables. Let D, be a variable which takes the value 0 if an individual has not earned a Master's degree, and a value 1 if they have earned a Master's degree. What would be the regression model that the researcher wants to test? A. S,= Po + B,D,+u, i=1, .. , n. O B. S,= Po + B, + u, i= 1, .. , n. OC. 1=6o +B1,S, + u, i= 1, .. , n. O D. 0=Bo +B, S, + u,, i= 1, .. , n. Suppose that a random sample of 160 individuals suggests that professionals without a Master's degree earn an average salary of $59,000 per annum, while those with a Master's degree earn an average salary of $80,000 per annum. The OLS estimate of the coefficient B, will be $ and that of B, will be $ Click to select your answer(s). DELLJackson finds that the heavier a person is, the higher his pulse rate tends to be. A linear regression model he built suggests that 20-kilogram differences in weight correspond to differences in pulse rate of 5 beats per minute. Which of the following must be true and explain your answer. (I) The correlation coefficient between body weight and pulse rate is 1/4. (II) Your pulse rate slows down 3 beats per minute if your weight decreases by 12 kilograms.