Consider a set of data (x₁, y₁), i = 1, 2, ..., n and the simple linear regression model given by:Yi = Bo + B₁x₁ + εiwith E() = 0, Var(ε;) = o² and all &'s are independent and normally distributed.Suppose further that a random sample of size 10 is selected and the fitted regression equation isobtained:withSB₁d)e)f)= 0.071 and SSxx = 1568.625.ŷi 2.106 0.933x₁Calculate and interpret the correlation coefficient.Derive the variance of w where w = ₁(x₁-x)]10 SS.xx+ ₁.Find the value of the variance of w in e) if Var (₁) is known to be 9.

Given that n=10, y^=2.106-0.933xi, sβ^1=0.071 and SSx=1568.625. Here β^0=2.106 and β^1=-0.933. We…

Answered: Consider a set of data (x₁, y₁), i = 1,…

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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Consider a simple linear regression model, Y₁ = Bo + B₁X₁ + ₁ for i=1,2,...,n with the usual random error term (&) assumptions. Suppose that hypotheses Ho: P₁ = 0 against H₁:₁ <0 were tested and Ho: B₁ = 0 was rejected. Assume ₁e₁² = 0. ei i) Briefly explain what the conclusion of the test means for the values of Y given the values of X. -1 ii) Draw an example of a scatter plot with the fitted regression line for the problem mentioned above. iii) Calculate and interpret the correlation coefficient for the problem at hand.
Consider the regression equation with quantitative predictor variable x1 and indicator variables x2 and x3, corresponding to one qualitative predictor variable. Interpret the hypothesis H0: β2 = 0 in terms of the regression lines associated with the three possible values of the qualitative predictor variable.
(Yi, X1i, X2i) satisfy the assumptions. You are interested in β1, the causal effect of X1 on Y . Suppose that X1 and X2 are uncorrelated. You estimate β1 by regressing Y onto X1 (so that X2 is not included in the regression). Does this estimator suffer from omitted variable bias? Explain.
Consider the points in the plane: (1,2) (2,3) (3,5) (4,4) (5,7) (7,8) (i) Compute the correlation coefficient. (ii) Compute the equation for the regression line.
5
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?
)A county real estate appraiser wants to develop a statistical model to predict the appraised value of 3) houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: E(u) = Bo + Bix, where y = appraised value of the house (in thousands of dollars) and x = number of rooms. Using data collected for a sample of n = 73 houses in Fast Meadow, the following results were obtained: y = 73.80 + 19.72x What are the properties of the least squares line, y = 73.80 + 19.72x? A) Average error of prediction is 0, and SSE is minimum. B) It will always be a statistically useful predictor of y. C) It is normal, mean 0, constant variance, and independent. D) All 73 of the sample y-values fall on the line.

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