(a) Calculate and write out the least-squares regression equation. (b) Calculate a 90% confidence interval for the slope ?1 of the regression. (c) Test the hypothesis that the altitude of origin...

(a) Calculate and write out the least-squares regression equation.

(b) Calculate a 90% confidence interval for the slope ?1 of the regression.

(c) Test the hypothesis that the altitude of origin affects the dark respiration rate. Write down the pair of hypotheses, specify the test statistic value or the P-value and state your conclusion of the test. Use ?=0.05

(d) For a batch of bugs collected at an altitude of 720 meters, what is the plausible range of the dark respiration rate? Provide an appropriate 95% interval (confidence interval or prediction interval).

(e) What is the sample correlation coefficient?

Extracted text: The rowan (Sorbus aucuparia) is a tree that grows in a wide range of altitudes. To study how the tree adapts to its varying habitats, researchers collected twigs with attached buds from 12 trees growing at various altitudes in North Angus, Scotland. The buds were brought back to the laboratory and measurements were made of the dark respiration rate. The accompanying table shows the altitude of origin (in meters) of each batch of buds and the dark respiration rate (expressed as µl of oxygen per hour per mg dry weight of tissue). ALTITUDE OF RESPIRATION ORIGIN X (m) RATE Y (µl/hr × mg) 90 0.11 230 0.20 240 0.13 260 0.15 330 0.18 400 0.16 410 0.23 550 0.18 590 0.23 610 0.26 700 0.32 790 0.37