Linear Regression
Solve the following problem:
In biology, there is an approximate rule, called the bioclimatic rule for temperate climates,that has been known for a couple of hundred years. This rule states that in spring and early summer, periodic phenomena such as blossoming of flowers, appearance of insects, and ripening of fruit usually come about 4 days later for each 500 feet of altitude. Stated as a formula, for where d is the change in days and h is the altitude (in thousands of feet). To test this rule, an experiment was set up to record the difference in blossoming time of the same type of apple tree at different altitudes. A summary of the results is given in the table.
h d
0 0
1 7
2 18
3 28
4 33
a. Use your calculator to find the Linear Regression model relating h and d to four decimal places. Does the bioclimatic rule, , appear to be approximately correct?
b. Sketch a graph on your calculator (not here) showing the scatter plot and line-of-best-fit. What are the units of measure for each axes? Distinguish your answer choices.
c. Clearly interpret the ratio-value of the slope for the model you found in part (a).
(hint: think of the units of measure for the slope)
d. How much longer will it take this type of apple tree to blossom at 3.5 thousand feet than at sea level? (Use the model found in part (a).) Show your algebraic work.
keywords: scatterplot