Question

Let x = day of observation and y = number of locusts per square meter during a locust infestation in a region of North Africa. x 2 3 5 8 10 y 2 3 12 125 630

(a) Draw a scatter diagram of the (x, y) data pairs. Do you think a straight line will be a good fit to these data? Do the y values almost seem to explode as time goes on? No. A straight line does not fit the data well. The data seem to explode as x increases. Yes. A straight line seems to fit the data well. The data seem to explode as x increases. No. A straight line does not fit the data well. The data does not seem to explode as x increases. Yes. A straight line does not fit the data well. The data seem to explode as x increases.

(b) Now consider a transformation y' = log (y). We are using common logarithms of base 10. Draw a scatter diagram of the (x, y') data pairs and compare this diagram with the diagram of part (a). Which graph appears to better fit a straight line? The two diagrams are the same. The transformed data fit a straight line better. The two diagrams are different. The transformed data does not fit a straight line better. The two diagrams are the same. The transformed data does not fit a straight line better. The two diagrams are different. The transformed data fit a straight line better.

(c) Use a calculator with regression keys to find the linear regression equation for the data pairs (x, y'). What is the correlation coefficient? (Use 3 decimal places.) y' = + x r =

(d) The exponential growth model is y = αβx. Estimate α and β and write the exponential growth equation. (Use 3 decimal places.) α = β = y hat = · x

Answer 1