# F test and t test in linear regression model

F test and t test are performed in regression models.

In linear model output in R, we get fitted values and expected values of response variable. Suppose I have height as explanatory variable and body weight as response variable for 100 data points.

Each variable (explanatory or independent variable, if we have multiple regression model) coefficient in linear model is associated with a t-value (along with its p value)? How is this t-value computed?

Also there is one F test at the end; again I am curious to know about its computation?

Also in ANOVA after linear model, I have seen a F-test.

Although I am new statistics learner and not from statistical background, I have gone through with lots of tutorials on this. Please do not suggest for going me with basic tutorials as i have already done that. I am only curious to know about the T and F test computation using some basic example.

• What's a 'predictory' variable? From your text, it actually sounds like you mean 'response variable' – Glen_b -Reinstate Monica Jul 5 '13 at 6:45
• yes ! response variable or independent variable . I am editing it . thanks – bioinformatician Jul 5 '13 at 6:52
• Whoah. Response variable = dependent variable = y-variable. Independent variable = explanatory variable = predictor variable = x-variable. Which is it? – Glen_b -Reinstate Monica Jul 5 '13 at 6:54
• Thanks Glen_b, I am delighted with the learning of types of variables in regression models andthe answer given below by Maaten buis made me clear the concept. – bioinformatician Jul 5 '13 at 8:59
• @bioinformatician Here are lists of terms that may help you. Let's start with synonyms for "dependent variable" = "explained variable", "predictand", "regressand", "response", "endogenous", "outcome", "controlled variable". Next are some synonyms for "explanatory variable" = "independent variable", "predictor", "regressor", "stimulus", "exogenous", "covariate", "control variable". Some of these terms are more popular than others across different disciplines. – Graeme Walsh Jul 5 '13 at 10:23

The misunderstanding is your first premise "F test and $t$-test are performed between two populations", this is incorrect or at least incomplete. The $t$-test that is next to a coefficient tests the null hypothesis that that coefficient equals 0. If the corresponding variable is binary, for example 0 = male, 1 = female, then that describes the two populations but with the added complication that you also adjust for the other covariates in your model. If that variable is continuous, for example years of education, you can think of comparing someone with 0 years of education with someone with 1 years of education, and comparing someone with 1 years of education with someone with 2 years of education, etc, with the constraint that each step has the same effect on the expected outcome and again with the complication that you adjust for the other covariates in your model.