1. Consider the regression modelY₁ = B₁ + B₁X₁; + B₂X₂; + &iTransform the regression so that you can use a t-statistic to test the followingrestrictions(a) B₁ = B₂(b) B₁ + a₂ = 0, a is a constant(c) B₁ + B₂ = 1 (Hint: You must redefine the dependent variable in the regression.)

Answered: Image /qna-images/answer/59b4a51e-081c-44ea-a601-e69e29d212f8.jpg

Answered: 1. Consider the regression model Y₁ =B₁…

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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c) Give the expression of R˜^2 in terms of R^2 , and justify your answer.
3
Q2 (a)State in algebraic notation and explain the assumption about the classical linear regression models disturbances that are referred to by the term ‘homoscedasticity’. (b)What would the consequence be for a regression model if theerrors were not homoscedastic? (c) How might you proceed if you found that (b) were actually the case? (d) What do you understand by the term ‘autocorrelation’?
A study was conducted to see whether heart rate (y) on swimmers linearly related to their age (x1) and swimming time for 2000 meters (x2). A random sample of ten swimmers was selected and the result is shown in the following Microsoft Excel output. (a)Interpret the value of R2 from the output. (b)Conduct a hypothesis test to test whether the linear regression model is fit or not using a = 0.05. (c)Calculate the 95% confidence interval for the coefficient value for age.
Detail all the steps involved in testing the hypothesis below for the linear regression model y = XB + e, where X = (50 x 6) for two cases. Ho: X3B3 + x4B4 = 0 На: x3B3 + x4B4 # 0
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?
Some non-linear regressions can also be estimated using a linear regression model (using 'linearization'). Assume that the data below show the selling prices y (in dollars) of a certain equipment against its age x (in years). We'd like to fit a non-linear regression in the form y = cd* to estimate parameters c and d from the data by linearizing the model through In y In c+ (In d)x = b, + b, x. y y 6381 3 5394 5673 4980 2 5740 4896 (Click the button to copy or download the data.) Using Excel ot other software, the non-linear regression model y = cd can be estimated as: y = D*. (Round c and d to four decimal places, inlcuding any zeros.)
the following regression table where the dependent variable is the demandfor massage services in one city in the United States. Specifically, the dependent variable is the number of customers per hour (Models 1 and 2) or per day (Models 3 and 4). a) Explain why the coefficient for Population/1,000 in Model 2 is very different from the one in Model 4?
The table shows the numbers of new-vehicle sales (in thousands) in the United States for Company A and Company B for 10 years. The equation of the regression line is ModifyingAbove y with caret equals 0.993 x plus 1 comma 195.82y=0.993x+1,195.82. Complete parts (a) and (b) below. New-vehicle sales left parenthesis Company Upper A right parenthesis comma x(Company A), x 4 comma 1674,167 3 comma 8823,882 3 comma 5693,569 3 comma 4433,443 3 comma 2993,299 3 comma 1173,117 2 comma 8372,837 2 comma 4982,498 1 comma 9401,940 2 comma 0842,084 New-vehicle sales left parenthesis Company Upper B right parenthesis comma y(Company B), y 4 comma 9204,920 4 comma 8444,844 4 comma 8374,837 4 comma 7104,710 4 comma 6754,675 4 comma 4284,428 4 comma 6604,660 3 comma 8323,832 2 comma 9272,927 2 comma 7532,753 Question content area bottom Part 1 (a) Find the coefficient of determination and interpret the result.…
A professor has found that scores on the midterm exam in her classes predict scores on the final exam. The regression constant in the linear prediction rule for predicting final exam scores from midterm exam scores is 31 and the regression coefficient is 0.5. Complete parts (a) through (k) below. (a) Indicate the predictor variable.
Find the quadratic regression curve through the following points (2, 5), (3, 5), (5, 3) y = 3.0000x? 0.3333x + 1.6667 y = 3.0000x2 + 1.6667x – 0.3333 O y = -0.3333x2 + 1.6667x + 3.0000 O y = 1.6667x2 – 0.3333x + 3.0000

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