Height and age of pine trees
A fit of height in metres on age in years for 50 trees gives intercept 5.5990 (standard error omitted, t=6.082) and slope 3.3949 with standard error 0.3899.
Write the fitted line and the predicted height at age 4.
The t statistic for the slope is 3.3949/0.3899. On 48 degrees of freedom its two-sided p-value is about 1.92\times 10^{-11}. Is there a linear association?
Worked answer (click to show)
The fitted line is \widehat{\mathrm{height}}=5.599+3.395\times\mathrm{age}. At age 4 the prediction is 5.599+3.3949\times 4=19.18 metres. The slope’s p-value is far below 0.05, so the fit shows a linear association between age and height.