A (hypothetical) study is conducted in which scientists grow a certain variety of corn under controlled conditions. The height of each plant is measured as well as the total number of kernels produced by the plant during one growing season. The plants have an average height of 12 feet with a standard deviation of 2 feet. The plants have a yield of 800 kernels on average, with a standard deviation of 100 kernels. The correlation between the two variables is r = 0.7.

A scatterplot is made with height on the horizontal axis and yield (number of kernels) on the vertical axis. The scatter diagram is football shaped, and histograms of height and yield both have a shape similar to the normal curve. The regression line for predicting the yield from the height of the plants is drawn through the scatter.

(a) A plant that is at the 90th percentile in terms of yield has _______ kernels.

(b) A plant that is at the 90th percentile in terms of height has a predicted yield of _____ kernels and is at the _____ percentile in terms of yield.

(c) A plant is at the 90th percentile in terms of both height and yield. Relative to plants of the same height, its yield is (circle one) (i) less than (ii) equal to (ii) greater than (iv) impossible to compare to

the estimated average value for the group calculated using the regression line. Justify your answer in terms of where these values fall relative to the SD line and regression line.

(d) Find the slope and intercept of the regression line. Be sure to include the correct units. Slope = _____________________________ Intercept = __________________________

(e) Is it appropriate to interpret the intercept of the regression line in this example? Why or why not?

I need some help answering these questions from my lab assignment. I also need to show my working out.