- Thread starter dfrisch
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I am going to assume you are referring to the F-statistic associated with the ANOVA summary for the full regression model.

With that in mind, this F-statistic tests the following null hypothesis:

H[0]: Beta1 = Beta2 = ... = BetaK = 0.

That is, the population parameters associated with the independent variables are all simultaneously equal to zero. In words, under H[0], it's states that you will get no help in predicting Y (the dependent variable) from the independent variables and that the best predictor of Y is the mean of Y (YBar).

That said, if you're referring to some other F-Statistic, then you're going to have be more specific and explain what statistic you're referring to (e.g. an F statistic associated with a change in R^2, for example).

Residual standard error: 365.4 on 18 degrees of freedom

Multiple R-squared: 0.9933, Adjusted R-squared: 0.9914

F-statistic: 531.2 on 5 and 18 DF, p-value: < 2.2e-16

This is the F-statistic I am looking for. I believe it needs to show a linear relationship between the y and x variables. If it doesn’t then the model is not appropriate for multiple regression. Or at least that is what I have read. Any insight into this?

Residual standard error: 365.4 on 18 degrees of freedom

Multiple R-squared: 0.9933, Adjusted R-squared: 0.9914

F-statistic: 531.2 on 5 and 18 DF, p-value: < 2.2e-16

This is the F-statistic I am looking for. I believe it needs to show a linear relationship between the y and x variables. If it doesn’t then the model is not appropriate for multiple regression. Or at least that is what I have read. Any insight into this?

What this tells me is that you're running a regression with 5 independent variables with N=24 data points.

Your sample size is too small! With this sample size you should not have any more than 1 or 2 (max) independent variables. Or, is this a homework assignment???

Next, the important statistics are the t-statistics associated with each of the regression coefficients. Look at the p-values for each. In so doing, try and reduce your I.V.'s.

Note: The overall F-statistic is of little use here. It's essentially demonstrating that the R^2 is signicantly greater than zero.

What this tells me is that you're running a regression with 5 independent variables with N=24 data points.

Your sample size is too small! With this sample size you should not have any more than 1 or 2 (max) independent variables. Or, is this a homework assignment???

Next, the important statistics are the t-statistics associated with each of the regression coefficients. Look at the p-values for each. In so doing, try and reduce your I.V.'s.

Note: The overall F-statistic is of little use here. It's essentially demonstrating that the R^2 is signicantly greater than zero.

Your sample size is too small! With this sample size you should not have any more than 1 or 2 (max) independent variables. Or, is this a homework assignment???

Next, the important statistics are the t-statistics associated with each of the regression coefficients. Look at the p-values for each. In so doing, try and reduce your I.V.'s.

Note: The overall F-statistic is of little use here. It's essentially demonstrating that the R^2 is signicantly greater than zero.

What I'm most interested in here is what I need to be concerned about with the F-Statistic when running regression analyses for the future. I feel like this is something I need to be aware of so I don't make a poor model that is not actually showing what my goals are, and I'm concerned about what I don't know that I don't know.... Thanks.

Unfortunately, no. It's not homework, but I just pulled a small amount of data together for an example of the F-statistic. Right now, you are talking a little over my head with some of that stuff since I am learning this as I go in order to understand how to show that certain coefficients are not (hopefully) predictors of salary for work.

What I'm most interested in here is what I need to be concerned about with the F-Statistic when running regression analyses for the future. I feel like this is something I need to be aware of so I don't make a poor model that is not actually showing what my goals are, and I'm concerned about what I don't know that I don't know.... Thanks.

What I'm most interested in here is what I need to be concerned about with the F-Statistic when running regression analyses for the future. I feel like this is something I need to be aware of so I don't make a poor model that is not actually showing what my goals are, and I'm concerned about what I don't know that I don't know.... Thanks.

Hi

The F-statistic must be interpreted with its p-value. The F-statistics tells us whether the overall regression (all the independent variables combined in the model) is statistically significant (there is a significant joint relationship). If the p-value is less than .05, as in your case, it supports this. After that you must look at the individual regression coefficients (their corresponding p-value) of each predictor variable to determine which variable is statistically significant. Although the F-statistic is significant, it doesn't mean that all variables would be significant - it just measures the joint effect of those variables. It is really saying that at least one of those predictors are significant in the model; so you have to determine individual significant effects, after inspecting the F-statistic. If the F-statistic is non-significant ( p > .05), you just conclude that the overall model is not significant - and there is no relationship whatsover.