QUESTION 1 In the SLR model, suppose the dependent variable (Y) represents the quantity consumed of apples in a particular area in tones, and the explanatory variable (X1) is the average price of apples in that area in £. If this model is estimated by OLS, then the estimated slope b1_hat, represents: by how many tones consumption of apples will change, if the average price of apples increases by £1 the predicted change in the consumption of apples (in kilos), if the average price of apples increases by £1 the predicted change in the price of apples (in £), if consumption of apples increases by 1 tone by how many tones consumption of apples is predicted to change, for a £1 increase in the average price of apples QUESTION 2 Suppose in the SLR model, the dependent variable (Y) represents 'the price of a house in £1,000', and the explanatory variable (X1) represents ‘the number of rooms in the house’. The estimated regression model is: Yhat =51.45 + 7.45*X1. According to this model, what is the predicted increase in the price of a house, if we add three rooms to a house? £73800 £7450 £22350 £7.45 QUESTION 3 Suppose you have an SLR model with the sample mean of the dependent variable (Y) being equal to 13.4, the sample mean of the explanatory variable (X1) being equal to 22.5, and the OLS estimate for the slope coefficient (b1_hat) being equal to 0.25. What is the value of the OLS estimate for the intercept (b0_hat) in this model? We cannot calculate it with the information provided It is 7.775 It is 19.025 It is 19.15

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

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 1

In the SLR model, suppose the dependent variable (Y) represents the quantity consumed of apples in a particular area in tones, and the explanatory variable (X1) is the average price of apples in that area in £. If this model is estimated by OLS, then the estimated slope b1_hat, represents:

by how many tones consumption of apples will change, if the average price of apples increases by £1
the predicted change in the consumption of apples (in kilos), if the average price of apples increases by £1
the predicted change in the price of apples (in £), if consumption of apples increases by 1 tone
by how many tones consumption of apples is predicted to change, for a £1 increase in the average price of apples

QUESTION 2

Suppose in the SLR model, the dependent variable (Y) represents 'the price of a house in £1,000', and the explanatory variable (X1) represents ‘the number of rooms in the house’. The estimated regression model is: Yhat =51.45 + 7.45*X1.

According to this model, what is the predicted increase in the price of a house, if we add three rooms to a house?

£73800
£7450
£22350
£7.45

QUESTION 3

Suppose you have an SLR model with the sample mean of the dependent variable (Y) being equal to 13.4, the sample mean of the explanatory variable (X1) being equal to 22.5, and the OLS estimate for the slope coefficient (b1_hat) being equal to 0.25. What is the value of the OLS estimate for the intercept (b0_hat) in this model?

We cannot calculate it with the information provided
It is 7.775
It is 19.025
It is 19.15

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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