What is the meaning of the f-statistic and f test, Mathematics

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You are given the following regression results estimating the demand for widgets based on time series data for the past 40 months.

Qt = 2.5 - 0.3 x Pt + 12 x Mt

Where Qt represents the quantity of widgets sold per period t, Pt represents the price of widgets during period t, and Mt represents average household income of customers during period t.

You are also given the following information about the regression results

R2 = 0.75              F-statistic = 23                   Durbin-Watson (d) statistic = 0.66
standard deviation of constant = 0.52;               standard deviation of P = 0.16
standard deviation of M = 2.0

a. Which of the independent variables are statistically significant at the 5% level?

b. Can you reject the null hypothesis that price does not affected quantity demanded? Can you reject the null hypothesis that income does not affect quantity demanded?

c. What proportion of total variation in Q is explained by the regression equation?

d. Is the F-statistic significant at the 5% level? What is the meaning of the F-statistic and F test?


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