6. (a) Show that in the simple linear regression setting, the usual F test statistic of Ho: B1 = 0 can bewritten asR (n – 2)F1- R²(b) In a simple linear regression with n= 300, how large must R² be in order for there to be significantevidence against the null hypothesis from a), at the 5% significance level.

Given the F test statistic of H0 : β1=0 as F=R2n-21-R2

Answered: 6. (a) Show that in the simple linear…

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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In order to test for the significance of a regression model involving 10 independent variables and 100 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are?
4. The following regression is fitted using variables identified that could be related to tuition charges ($) of a university. TUITION = a+ B ACCEPT + y MSAT + 1 VSAT Where ACCEPT = the percentage of applicants that was accepted by the university, MSAT = Median Math SAT score for the freshman class and VSAT = Median English SAT score for the freshman class. The data was processed using MNITAB and the following is an extract of the output obtained: Predictor Coef StDev T P Constant -26780 6115 -4.38 0.000 ACCEPT 116.00 37.17 * 0.003 MSAT -4.21 14.12 VSAT 70.85 15.77 -0.30 4.49 0.767 ** S = 2685 R-Sq = 69.6% Analysis of Variance R-Sq (adj) = 67.7% Source DF SS MS F P Regression 3 808139371 Residual Error 49 353193051 269379790 7208021 37.37 0.000 Total 52 1161332421 a) Write out the regression equation. b) State the dependent and independent variable(s) c) Fill in the blanks identified by ** and ****. d) Is B significant, at the 10% level of significance? e) State one limitation of using…
A recent Gallup survey of a random sample of Americans (18 and older) found that the average number of alcoholic drinks consumed per week (drinks) by males was 4.2 and by females was 1.4.[1] Suppose we use the underlying survey data to estimate a least-squares regression of the average number of drinks a person reports consuming per week (Drinks;) on a dummy variable equal to 1 if i is female and O otherwise (Female;). (Assume all respondents identify as either male or female.) The estimated regression line equation can be written as: Drinks = a +bFemale Alcohol Consumption by Gender Because Female is a dummy variable, the problem provides us with enough information to figure out the exact regression line equation. What is the numerical value of a?
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29)
A pharmaceutical company is examining the relationship between dosage of a new pain-relief medication and the time it takes for patients to experience pain relief from a headache. Various dosages ranging from 200 to 1,200 milligrams (mg) in 100-milligram increments were given to 41 randomly selected patients, and the time until relief was measured in minutes. A check of the conditions necessary for inference for the slope of a regression line shows that they are met. A 95 percent confidence interval for the slope of the regression line relating the dosage, x, to the time until relief, y, is given by (−4.15,−2.27). Based on the confidence interval, which of the following claims is supported? A 100 mg increase in dosage results in a decrease in the time until relief by more than two minutes on average. A A 100 mg increase in dosage results in a decrease in the time until relief by more than four minutes on average. B There is not a linear relationship…
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