Test whether a linear relation exists between age and total cholesterol at the \(\alpha=0.05\) level of significance using the data in Table 1 from Example 1.

Approach Verify that the requirements to perform the inference are satisfied. Then follow Steps 1 through 5.

Data from Example 1

A family doctor is interested in examining the relationship between a patient's age and total cholesterol (in \(\mathrm{mg} / \mathrm{dL}\) ). He randomly selects 14 of his female patients and obtains the data presented in Table 1. The data are based on results obtained from the National Center for Health Statistics. Draw a scatter diagram, compute the correlation coefficient, find the least-squares regression equation, and determine the coefficient of determination.

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Table 1 Age,. Total Cholesterol, y Age,.x Total Cholesterol, y 25 180 42 183 25 195 48 204 28 186 51 221 32 180 51 243 32 210 58 208 32 197 62 228 38 239 65 269