2. Suppose we’ve conducted a regression to estimate a demand function, with quan

Question

2. Suppose we’ve conducted a regression to estimate a demand function, with quantity demanded as the dependent variable and price as the independent variable. The coefficient of the independent variable is -4.28, and the standard error of the coefficient is 1.33. Using the procedures we have discussed in class:

a. Explain and interpret the independent variable and its coefficient in the equation.

b. Determine, explain and interpret the statistical significance of price as an independent variable in this regression.

Explanation / Answer

Solution:

(a) We know general linear regression equation is ,

y = b0 + b1 *x

Given:

x : Independent variable = Price

y : Dependent variable = Quantity demanded

b1 : coefficient of x = -4.28

standard error = Se = 1.33

(b) Now we have to test significance of x in the regression equation.

Null hypothesis,

H0: 1 = 0

Alternative hypothesis

Ha: 1 0

Degrees of freedom. For simple linear regression (one independent and one dependent variable), the degrees of freedom (DF) is equal to:

DF = n - 2

You have not given n (sample size) in your question. For now I assume n = 100.

DF = 100-2 = 98

Test statistic: The test statistic is a t statistic (t) defined by the following equation.

t = b1 / Se

Hence t = -4.28 / 1.33

t = -3.2180

Here we take absolute t = 3.2180

Now we have to find p-value.

Using excel , =2*TDIST(3.218,98,1)

P-value = 0.0017

Here p-value < 0.05

Hence we reject null hypothesis.

Conclusion: Independent variable is significant in regression equation.

Above all calculations done assuming n = 100 as it is not given in question.

Done

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