Confidence Interval for Regression Slope

Consider the following statements regarding a confidence interval for $\beta$, the slope of a population regression line.

I. The interval is constructed using the formula $b \pm t^{*}\times s_b$, where $t^{*}$ is the critical value from a t-distribution with $n-2$ degrees of freedom.

II. As the standard error of the slope increases, the width of the confidence interval for $\beta$ increases.

III. A wider confidence interval indicates stronger evidence of a linear relationship between the explanatory and response variables.

Which of these statements is/are correct?