2. For the regression modelY₁ = 3x₂ + Eii=1,2,..., ni.e. a straight line through the origin with the usual assumptions about the errors. InExercise Sheet 2, you found the least squares estimator of 3₁ and its mean and variance.(a) Derive the form of a 100(1-a)% confidence interval for B.(b) If we define the residual e; = Y; -ßx;, show thatE[e₁] = 0and thatVar[e;]=2² [1-2²]

Given the regression model Yi=βxi+εi i=1, 2, . . ., n

Answered: 2. For the regression model Y₁ = 3x₂ +…

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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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?
Suppose that you run a regression of Y, on X, with 110 observations and obtain an estimate for the slope. Your estimate for the standard error of ₁ is 1. You are considering two different hypothesis tests: The first is a one-sided test: Ho: B1-0, Ha: 31>0, a = .05 The second is a two-sided test: Ho: 31-0, Ha: B1 0,a = .05 (a) What values of , would lead you to reject the null hypothesis in the one-sided test? (b) What values of , would lead you to reject the null hypothesis in the one-sided test? (c) What values of would lead you to reject the mill hypothesis in the one-sided test, but not the two-sided test? (d) What values of 3 would lead you to reject the null hypothesis in the two-sided test, but not the one-sided test?
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…
Find the least square regression line.
Suppose we have a multiple regression model with 2 predictors and an intercept. (Without any interaction or higher order terms, we have only the 2 predictors in the model and the intercept.) We have only n= 6 observations (so it would be rather silly to fit this model to this data, but let's pretend it is reasonable). We find the values of the first 5 residuals are: 2.6, 2.3, 2.5, -1.5, -1.4 What is the value of MSRes for this multiple regression model?
You forgot to JUSTIFY THE ANSWRRS LAST TIME
Students who complete their exams early certainly can intimidate the other students, but do the early finishers perform significantly differently than the other students? A random sample of 37 students was chosen before the most recent exam in Prof. J class, and for each student, both the score on the exam and the time it took the student to complete the exam were recorded. a. Find the least-squares regression equation relating time to complete (explanatory variable, denoted by x, in minutes) and exam score (response variable, denoted by y) by considering Sx = 15, sy = 17,r = 39.706, x = 90, ỹ = 78 b. The standard error of the slope of this least-squares regression line was approximately (Sp) is 20.13. Test for a significant positive linear relationship between the two variables exam score and exam completion time for students in Prof. J's class by doing a hypothesis test regarding the population slope B1. Write the null and Alternate hypothesis and conclude the results. (Assume that…
This table reports the regression coefficients when the returns of the size-institutionalownership portfolio (columns 1 and 2) returns are regressed on three variables: a constant(column 3), the stock market returns (column 4), and the change of the value weighted discountof the closed end fund industry (column 6). Columns 5 and 7 report the corresponding t-statistics of the coefficient estimates. Note that a t-statistic with an absolute value above 1.96means the coefficient estimate is significantly different from 0 at the 1% level. Column 8reports the R square of the regressions. Column 9 reports the mean institutional ownership ofeach portfolio. The last column reports the F-statistics for a multivariate test of the null hypothesis that the coefficient on ΔVWD in the Low (L) ownership portfolio is equal to theHigh (H) ownership portfolio. Two-tailed p-values are in parentheses. 1. What is the main finding of this Table? 2. What is the explanation for…

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