Answered: The Simple Linear Regression model is…

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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Question

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The Simple Linear Regression model is

Y = b0 + b1*X1 + u

and the Multiple Linear Regression model with k variables is:

Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u

Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term,

Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients.

QUESTION 4

Suppose we have an SLR model, where the dependent variable (Y) represents ‘how satisfied someone is with his/her life, from 0 to 100’ (the higher the value, the higher the satisfaction with life), and the explanatory variable (X1) represents ‘personal annual income in £1,000’. The estimated OLS regression line is:

Yhat = 33.2 + 0.74*X1.

According to this model, what is the predicted life satisfaction, for someone with personal annual income of £22,000?

A. 74 satisfaction units

B. 0.74 satisfaction units

C. 49.48 satisfaction units

D. 16313.2 satisfaction units

QUESTION 5

In the SLR model, suppose the explanatory variable (X1) represents how much a school spends per student (in £1000), and the dependent variable (Y) represents the average test score (in percent) in a standardised test in that school. Suppose you collect a sample of different schools and estimate this model by OLS. Then the estimated intercept b0_hat, represents:

A. by how much the average test score (in percent) is predicted to change, if spending per student in a school increases by £1000

B. The predicted spending per student for a school, if the average test score in that school is equal to 0%

C. the predicted average test score (in percent), for a school that spends £0 per student

D. the predicted average test score (in percent) in a school, irrespective of the spending per student in that school

QUESTION 6

Suppose you have the following data:

Y X

-1 4

-2 2

1 -1

4 -3

3 1