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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41. Which of the following is the multiple regression model for the data? (a) y = -0.11050 + 2.10797x1 + 0.40717x2 (b) y = -0.11050 + 0.40717x1 + 2.10797x2 (c) y = 0.23563 + 0.00062x1 + 0.23626x2 (d) none (e) y = -0.44187 + 2.42120x1 + 0.36135x2
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.
Consider a set of data (x₁, yi), i=1,2,..0 and the Simple linear regression equation given by : 4 y₁ = B₁+ B₁²x₁ The /s Standardized random variable of given by 2= B₂₁ - B²₁₂² FSSxx find the mean and the variance of Zo
5
11) A simple linear regression model based on 20 observations. The F-stat for the model is 21.44 and the SSE is 1.41. The standard error for the coefficient of X is 0.2. a) Complete the ANOVA table. b) Find the t-stat of the co-efficient of X c) Find the co-efficient of X.
Find the least square regression line.
Suppose that I want to estimate the effect of x₁ on y. Consider the univariate regression line: how to calculate a and b₁ using OLS? y = a + b₁x₁
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?
Proposed Method: 1. Simple linear regression 2. One sample t-test Regression equation: y; = B0 + B1z; + € i = 1(1)30 Where y; Quarterly sales data from the ith gas station z; the size of the population of cars in the ith gas station B0 and B1 are unknown parameters which are to be estimated by the model. Null hypothesis: HO: B1 = 0 Alternative Hypothesis: H1: B1 + 0 1 forgot how to do this because its been a while since doing a statistics class

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