In multiple regression with k independent variables, the t-tests of the individual coefficients allow us to determine whether $\beta _ { i } \neq 0$ (for i = 1, 2, …, k), which tells us whether a linear relationship exists between $x _ { i }$ and y.

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The t-tests for individual coefficients in multiple regression test the null hypothesis that each coefficient $\beta_i$ is equal to zero, indicating whether there is a statistically significant linear relationship between each independent variable $x_i$ and the dependent variable y.

In Multiple Regression with K Independent Variables, the T-Tests of the Individual