Coastal State University is conducting a study regarding the possible relationship between the cumulative grade point average and the annual income of itsrecent graduates. A random sample of 147 Coastal State graduates from the last five years was selected, and it was found that the least-squares regressionequation relating cumulative grade point average (denoted by x, on a 4-point scale) and annual income (denoted by y, in thousands of dollars) wasy = 37.79+5.51x. The standard error of the slope of this least-squares regression line was approximately 2.10.Test for a significant linear relationship between grade point average and annual income for the recent graduates of Coastal State by doing a hypothesis testregarding the population slope B1. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions aresatisfied.) Use the 0.05 level of significance, and perform a two-tailed test. Then complete the parts below.(If necessary, consult a list of formulas.)(a) State the null hypothesis H and the alternative hypothesis H.H :H :0OSO(b) Determine the type of test statistic to use.O20O

Answered: Image /qna-images/answer/b1c2e4d2-ab45-4c6b-8bb2-8ba2840f8922.jpg

Answered: Coastal State University is conducting…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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what is a confidence coefficinent for a simple linear regression line whoes alpha =0.05 and line is y(hat)=-7.45-10x
Data on 220 reported crimes is collected from district X in 2016. Suppose CS denotes the total cost to the state of offering crime protection services to this district (in thousand dollars), LEOP denotes the number of law enforcement officers on patrol, DTP denotes the damage to public and private property (in thousand dollars), CCTV denotes the number of CCTV cameras installed in the district, and Prison denotes the number of prison inmates The following table shows the results of a few regressions of the total cost to the state. Dependent variable: total cost to the state (in thousand dollars) Regressor (1) (2) (3) (4) 12.32 17.99 14.55 18.1 LEOP (0.52) (0.84) (2.25) (0.82) 0.73 0.59 0.75 DTP (0 12) (0.04) 0.73 (0.06) CCTV (0.13) 2.11 2.12 (0.39) 288.5 (4 14) Prison (0.5) 182.5 191.6 219.95 Intercept (11.52) (6.68) (5.26) 0.64 0.75 0.12 0.75 R 220 220 220 220 Heteroskedasticity-robust standard errors are given in parentheses under coefficients. Which of the following statements…
Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher’s salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below. (a) What proportion of the variation in MCAS score is explained by the explanatory variables? (b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly. (c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly. (d) Suppose a second regression model (Model 2) was generated using only…
If a scatterplot is created in excel, and a line of regression is fit along with a derived functional form, what does it mean to describe and interpret them? What conclusions would be made about relationships between two recorded variables?
The maintenance manager at a trucking company wants to build a regression model to forecast the time (in years) until the first engine overhaul based on four predictor variables: (1) annual miles driven (in 1,000s of miles), (2) average load weight (in tons), (3) average driving speed (in mph), and (4) oil change interval (in 1,000s of miles). Based on driver logs and onboard computers, data have been obtained for a sample of 25 trucks. A portion of the data is shown in the accompanying table. Time Miles Load Speed Oil 7.7 42.9 22.0 44.0 16.0 0.8 98.3 20.0 47.0 34.0 6.3 61.1 22.0 62.0 15.0 E Click here for the Excel Data File b. Estimate the regression model. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Time = Miles Load Speed oil + + d. What is the predicted time before the first engine overhaul for a particular truck driven 60,000 miles per year with an average load of 25 tons, an average driving speed of 53 mph, and 21,000 miles…
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.…
Acrylamide is a chemical that is sometimes found in cooked starchy foods and which is thought to increase the risk of certain kinds of cancer. The paper "A Statistical Regression Model for the Estimation of Acrylamide Concentrations in French Fries for Excess Lifetime Cancer Risk Assessment"+ describes a study to investigate the effect of frying time (in seconds) and acrylamide concentration (in micrograms per kilogram) in french fries. The data in the accompanying table are approximate values read from a graph that appeared in the paper. Frying Acrylamide Time Concentration 150 240 240 270 300 300 150 125 + 195 185 135 275 USE SALT (a) Find the equation of the least-squares line for predicting acrylamide concentration using frying time. (Round your answers to four decimal places.) ŷ = (b) Does the equation of the least-squares line support the conclusion that longer frying times tend to be paired with higher acrylamide concentrations? Explain. O No, the least squares regression line…
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A scientific foundation wanted to evaluate the relation between y= salary of researcher (in thousands of dollars), x1= number of years of experience, x2= an index of publication quality, x3=sex (M=1, F=0) and x4= an index of success in obtaining grant support. A sample of 35 randomly selected researchers was used to fit the multiple regression model. Parts of the computer output appear below. The p-value of the ANOVA F test will be very large, since it's clear that all of the variables are good predictors of salary very small, since it's clear that all of the variables are good predictors of salary very large, since it's clear that none of the variables are good predictors of salary very small, since it's clear that none of the variables are good predictors of salary
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A year-long fitness center study sought to determine if there is a relationship between the amount of muscle mass gained y(kilograms) and the weekly time spent working out under the guidance of a trainer x(minutes). The resulting least-squares regression line for the study is y=2.04 + 0.12x A) predictions using this equation will be fairly good since about 95% of the variation in muscle mass can be explained by the linear relationship with time spent working out. B)Predictions using this equation will be faily good since about 90.25% of the variation in muscle mass can be explained by the linear relationship with time spent working out C)Predictions using this equation will be fairly poor since only about 95% of the variation in muscle mass can be explained by the linear relationship with time spent working out D) Predictions using this equation will be fairly poor since only about 90.25% of the variation in muscle mass can be explained by the linear relationship with time spent…

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