True/False Questions Circle T or F for T rue or F alse. For full credit and rewa

Question

True/False Questions

Circle T or F for True or False. For full credit and reward for help, please provide a written answer using complete sentences for each question.

1.      T F In a simple linear regression, if the independent variable has a small variance, the estimated slope coefficient, b^, will have a large p-value.

2.      T F Demographic variables are included in an estimated demand function to proxy for tastes and preferences.

3.      T F The estimated intercept, ?, in any simple or multiple regression has the same units of measure as the dependent variable, yi.

4.      T F A trend variable in a linear regression model will shift the intercept up or down.

5. 5. T F In a simple regression, if the correlation between the dependent and independent variables is zero, the conditional mean of the dependent variable is equal to the unconditional mean.

Thank you to anyone able to help and I hope to hear from someone as soon as they can, I am trying to figure these out to reference for my test tomorrow. I am not sure how to properly state each of the answers and truly appreciate any help that anyone can give me in trying to help me with these questions.

Explanation / Answer

1) False

Reason: as small variance indicates t-statistic value for slope b^ is high . So p-value will be low. As high t-stat indicates low p-value

t-statistic of slope = mean of slope/sqrt(variance)

If t-statistic is very high, then as p- value =Probability (t >= t-stat) . So area after calculated t-stat will be low. So as p-value represents area of curve after t-stat, hence p-value will be low.

2)True

Demand function Q = f( price, income, tastes and preferneces)

So as price and income are directly observble, there is no problem. But for tastes and prefernces, demographic variables are included like , whether individual is kid or teen ( As if he is kid he likes toys. So if we are estimating demand function for toys, then we can include variable as whether is kid or not which represents demographic variable)

reason: For tastes and preferences, demographic variables are included in an estimated demand function

3) True

as y^ = a^ + b^*x (simple regression)

=> if x=0 so y^ = a^ ( so it must have same units as a)

similarly,

y^ = a^ + b1^*x 1+b2^*x2 ( multiple regression)

so if x=0, y^ =a^ ( so it must have same units as a)

reason : As estimated intercept represents average value of dependent variable when all independent variables are zero. hence it has same measure of dependent variable

4) True

equation with out trend y^ = a^+b^x

equation with trend y^ = a^+b1*t+b2^x ( introducing trend means adding time variable on right hand side)

so we if we plot to equations in graph, we can see that second equation will shift the intercept by b1*t as b1*t is on right hand side of second equation

Reason: As trend indictaes intercept+a*t. So it shifts the intercept

5)True

correlation =0 means there is no relation between dpendent and independent variable. Hence conditional mean is equal to unconditional mean ( this is by defnition)

Reason:if the correlation between the dependent and independent variables is zero, the conditional mean of the dependent variable is equal to the unconditional mean

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