Critical value for F test is 2.24 . t-test statistic for 'Displacement is -1.993
The t-test show whether two populations are statistically different from each other. ANOVA show whether three or more populations are statistically different from each other. Both of them uses the difference in means and the spread of the distributions (called variance) across groups.
We get a test statistic value (“t” or “F”, respectively) from t test and ANOVA. The value we get are converted into a “p-value.” A p-value is the probability that the null hypothesis (that both (or all) populations are the same) is true. We can say that, a lower p-value reflects a value more significantly different across populations.
t-test statistic for 'Displacement' = coefficients / standard error = -0.0176/0.00883 = -1.993
We find critical value with given significance level using F distribution table as 2.24
F Critical Value = the value found in the F-distribution table with n1-1 and n2-1 degrees of freedom and a significance level of α.
The question is incomplete. The complete question is
A researcher is interested to find out how the engine displacement, vehicle weight, and the type of transmission [i.e. automatic & manual] affect the automobile gasoline mileage. Type of transmission is represented by one dummy variable: automatic (=1, if transmission is automatic; = 0, if transmission is manual)
Part of the raw data and the regression output of 40 different car models are given below. ( see images).
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