Data were collected from a longitudinal study designed to investigate the relationship between blood sugar levels and brain shrinkage. The results of an analysis of the data for 22 observations are shown in the table below.

$$ \begin{array}{|l r r|} \hline \text{Term} & \text{Coef} & \text{SE Coef} \\ \text{Constant} & -15.668 & 6.154 \\ \text{Blood Sugar} & 0.161 & 0.073 \\ \hline \end{array} $$

Which of the following represents a 98 percent confidence interval for the slope of the least-squares regression line for brain shrinkage on blood sugar levels? Assume the conditions for inference are met.

Summary Submit

$$ \text{Confidence interval} : \text{statistic}\pm(\text{critical value})(\text{standard error of statistic}) $$ $$ = b\pm t^*(s_b) $$

Our statistic is the slope, or coefficient corresponding to blood sugar. The \(t^*\) value for a 98 percent confidence interval can be found in the table, with \(22-2=20\) degrees of freedom.

$$ = 0.161\pm 2.528(0.073)$$