The cost of attending your university/college has once again gone up. One of theadministrators at your university/college tells you that you pay more because thereputation of your institution is better than that of others. To investigate this hypothesis,you collect data randomly for 100 national universities and liberal arts colleges from the2000-2001 U.S. News and World Report annual rankings. Next you estimate thefollowing regression equation (p-values are in brackets).Cost = 7,311.17+3,985.20 i Reputation – 0.20 i Size(2,058.63) (664.58)(0.11)+ 8,406.79 i Dpriv – 416.38 i Dlibart – 2,376.51 i Dreligion(2,154.85)(1,121.92)(1,007.86)R²= 0.72The numbers in parentheses (brackets) are standard errors.Where:Cost is Tuition, Fees, Room and Board in dollarsReputation is the index used in U.S. News and World Report (based on a surveyof university presidents and chief academic officers), which ranges from 1("marginal") to 5 (“distinguished")Size is the number of undergraduate studentsDpriv, Dlibart, and Dreligion are separate dummy variables indicating whetherthe institution is private or not private, i.e. public [Dpriv]; a liberal arts college ornot liberal arts [Dlibart]; and has a religious affiliation or is not religious[Dreligion].(a) Interpret the coefficients of the variables below and test to determine whetheror not the coefficients are significantly different from zero at the alpha=5%level. (Show your work). What would be the problem if you could not claimthe coefficients are different from zero?(i)Reputation(ii)Dpriv(b) To save money, you are willing to switch from a private university to a publicuniversity, which has a ranking of 0.5 less and 10,000 more students. What is theeffect on your cost? (c) Does there seem to be a difference in cost between a liberal arts college andone that is not liberal arts? Explain.

Answered: The cost of attending your…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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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?
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?
Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
** had to resubmit this question because the first time the data was duplicated and reflected incorrectly. The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 1 2 3 4 5 5.5 6 Overall Grades 96 89 87 77 76 68 64 **Please circle the answer for each step so I don't get confused. Thanks in advance for helping me with the breakdown and notes** Step 1 of 6 : Find the…
What is the effect of this violation on the regression model? "The number of observations n is less than or equal to the number of parameters to be estimated"
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…
Suppose you wanted to test whether or not the payoff to an additional year of education was the same for men and women in the STEM majors. How would you set up your regression analysis in this case
You spilled water on your calculations from (a) and can't remember what your estimated regression parameters are. But you do have two possible estimated errors for each of your initial four observations:
A researcher was interested in investigating whether the parent-child interaction time (in hours) is a predictor of a child's cognitive development. A sample of 9 children shown their parent-child interaction time and cognitive tests scores as below. 1. Base on the regression equation, estimate the predicted cognitive level for a child whose parent interacts with him 6 hours per day?
The Life Insurance Company is attempting to model the weight, Y (in pounds), of a random sample of n=92 randomly selected adults using height, X1 (in inches), and gender, I2 (0 = Male 1=Female). In addition, as part of the research objective, we also wish to determine if the influence of height (X1) on weight (Y) depends on gender (I2) and vice versa. Write out the general regression equation for this model, based on the research objectives and information provided. Using the general equation from part A, write out the specific regression equation for a female. Using the general equation from part A, write out the specific regression equation for a male. If it was found that the influence of height on weight did NOT depend on gender, how would this change the equation given in part A of this problem? Rewrite the general equation from part A here.
If the R-squared for a regression model relating the outcome y to an explanatory variable x is 0.9. This implies that there is a positive linear relationship between y and x. True or false?
For the 2011 season, suppose the average number of passing yards per attempt for a certain NFL team was 6.1. Use the estimated regression equation developed in part (c) to predict the percentage of games won by that NFL team. (Note: For the 2011 season, suppose this NFL team's record was 7 wins and 9 losses. Round your answer to the nearest integer.)

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