Explanation

When testing a hypothesis about a single regression coefficient (in this case, testing whether β = 1), the appropriate test statistic is the t-statistic.

Why t-statistic?

• The t-statistic is used for testing hypotheses about individual regression coefficients
• Formula: t = (estimated coefficient - hypothesized value) / standard error
• In this case: t = (0.86 - 1) / 0.80 = -0.14 / 0.80 = -0.175

Why not the other options?

• Chi-square test statistic: Used for testing variance or goodness-of-fit, not individual coefficients
• F test statistic: Used for testing multiple coefficients simultaneously or overall model significance
• Sum of squared residuals: A measure of model fit, not a test statistic for coefficient hypotheses

Statistical Context

In linear regression, when testing H₀: β = β₀ against H₁: β ≠ β₀, the test statistic follows a t-distribution with n-k-1 degrees of freedom (where n is sample size and k is number of predictors).