A Random Sample of 79 Patients from a Walk-In Clinic

Multiple Choice

A random sample of 79 patients from a walk-in clinic records the low- and high-density cholesterol levels of the patients, labeled LDL and HDL, respectively. LDL is often referred to as "bad" cholesterol, while HDL is often referred to as "good" cholesterol. A researcher is interested in fitting the following linear regression curve to LDL and HDL levels:
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LDL_i = α+ β× HDL_i + Ɛ_i
Where the deviations Ɛ_i are assumed to be independent and Normally distributed with mean 0 and standard deviation σ. This model was fit to the data using the method of least squares. The following results were obtained from statistical software:
$$\begin{array} { | c | c | c | } \hline \text { Variable } & \text { Estimate } & \begin{array} { c } \text { Standard Error of } \\\text { Estimate }\end{array} \\\hline \text { Constant } & - 25 & 3.000 \\\text { HDL } & 0.75 & 0.025 \\\hline\end{array}$$ r² = 0.810, s = 50.
What is a 90% confidence interval for the slope β₁ in the simple linear regression model?

A) 0.75 ± 4.995
B) 0.75 ± 0.042
C) -25 ± 4.995
D) -25 ± 0.042