Sarah has some data and wants to run a linear regression model on it. Before she runs the test, s- knows she needs to check to make sure all conditions are met. Based only on the plots below, what condition is not met? Data Scatterplot Normal Probability Plot Residual Scatterplot
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?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?A business statistics professor would like to develop a regression model to predict the final exam scores for students based on their current GPAs, the number of hours they studied for the exam, the number of times they were absent during the semester, and their genders. The data for these variables are given in the accompanying table at the bottom of this page. a) Using Excel, construct a regression model using all of the independent variables. Create the dummy variable Gen, which equals 1 for a male and 0 for a female student ( this assignment is arbitrary) complete the regression equation for the model below, where y= Score, x1= GPA, x2= Hours, x3= Absenses, and x4= Gen. y= (__) + (__)x1 + (__)x2 + (__)x3 + (__)x4 b) Test the significance of the overall regression model using a= 0.10. c) interpret the meaning of the regression coefficient for the dummy variable. d) using the p-values, identify which independent variables are significant with a= 0.10. e) construct a regression…
- what is a confidence coefficinent for a simple linear regression line whoes alpha =0.05 and line is y(hat)=-7.45-10xThe sheet called HousePr contains data on prices of houses that have sold recently and two attributes of the house – the number of bedrooms and the size. Column 1 is the selling price of the house in thousands of dollars and column 2 is the size in hundreds of square feet.A. What is the expected price for a house with size 2000 square feet? Using relevant Excel output, discuss whether the margin of error of this expected price will be low or high.B. Using Excel, obtain the equation of the linear regression line that fits this data for price vs. number of bedrooms. Is the true slope different from zero?C. Which of these two variables – number of bedrooms or size, is the better predictor for price and why? Price SqrFoot Bedrooms731 21 4901 22 4736 16 3866 19 3697 12 2836 17 3694 17 3843 18 3721 15 4883 18 2913 17 3868 17 3642 17 3884 17 3810 16 2841 16 3779 17 4726 16 3667 14 2870 21 4834 16 2776 19 4681 14 2846 19 4917 20 4946 23 5813 20 4911 18 3723 17 3711 15 2897 19 4881 22 4863 19…Given a generic data set (x,y) with a linear regression. How do you determine if the y(dependent) will be less/greater than a certain value at a decided value of x?
- Suppose the athletic director at a university would like to develop a regression model to predict the point differential for games played by the men's basketball team. A point differential is the difference between the final points scored by two competing teams. A positive differential is a win, and a negative differential is a loss. For a random sample of games, the point differential was calculated, along with the number of assists, rebounds, turnovers, and personal fouls. Use the data in the accompanying table attached below to complete parts a through e below. Assume a = 0.05. a) Using technology, construct a regression model using all three independent variables. y = __ + (_)x1 + (_)x2 + (_)x3 + (_)x4 b) Test the significance of each independent variable using a= 0.10. c) interpret the p-value for each independent variable. d) Construxt a 90% confidence interval for the regression coefficients for each independent variable and interpret the meaning. e) Using the results from…A paper suggests that the simple linear regression model is reasonable for describing the relationship between y = eggshell thickness (in micrometers, µm) and x = egg length (mm) for quail eggs. Suppose that the population regression line is y = 0.125 + 0.007x and that ?e = 0.005. Then, for a fixed x value, y has a normal distribution with mean 0.125 + 0.007x and standard deviation 0.005. (a) What is the mean eggshell thickness for quail eggs that are 15 mm in length? ____ µm What is the mean eggshell thickness for quail eggs that are 17 mm in length? ____ µm (b) What is the probability that a quail egg with a length of 15 mm will have a shell thickness that is greater than 0.23 µm? _____ (c) Approximately what proportion of quail eggs of length 14 mm have a shell thickness of greater than 0.222? (Hint: The distribution of y at a fixed x is approximately normal. Round your answer to four decimal places.) ____ Approximately what proportion of quail eggs of length…For a set of data: x = (0,1,2,3,4,5,6) and y=(36, 28, 25, 24, 23, 21, 19), is it wise to use a linear regression to extrapolate data for x = 50? Solution: Since the coefficient of determination is 0.8582, the linear model is a reasonably good fit for the data, so extrapolation for any x-value is acceptable. What is wrong with this solution?
- A paper suggests that the simple linear regression model is reasonable for describing the relationship between y = eggshell thickness (in micrometers, µm) and x = egg length (mm) for quail eggs. Suppose that the population regression line is y = 0.185 + 0.007x and that ?e = 0.005. Then, for a fixed x value, y has a normal distribution with mean 0.185 + 0.007x and standard deviation 0.005. (You may need to use a table.) b)What is the probability that a quail egg with a length of 15 mm will have a shell thickness that is greater than 0.29 µm? (c)Approximately what proportion of quail eggs of length 14 mm have a shell thickness of greater than 0.281? (Hint: The distribution of y at a fixed x is approximately normal. Round your answer to four decimal places.) Approximately what proportion of quail eggs of length 14 mm have a shell thickness of less than 0.286? (Round your answer to four decimal places.)A researcher is hired to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance in miles between home and work for the employees. A sample of 10 employees was chosen and the results are listed in the chart below. Use the proper Data Analysis function in Excel to computethe regression equation needed to predict the number of missed days that could be expected foremployees who live certain distances away from the workplace. Distance to Work (miles): 1, 3, 4, 6, 9, 10, 12, 14, 14, 18 Number of Days Absent: 9, 6, 7, 7, 6, 4, 5, 3, 4, 2