Companies work hard to have their website listed at the top of an Internet search. Is there a relationship between a website’s position in the results of an Internet search (1 = top position,2=2nd position, etc.) and the percentage of people who click on the link for the website? Here are click-through rates for the top 10 positions in searches on a mobile device:

a. Make an appropriate scatterplot for predicting click-through rate from position. Describe what you see.

b. Use transformations to linearize the relationship. Does the relationship between click-through rate and position seem to follow an exponential model or a power model? Justify your answer.

c. Perform least-squares regression on the transformed data. Give the equation of your regression line. Define any variables you use.

d. Use your model from part (c) to predict the click-through rate for a website in the 11^th position.

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Click- Click- through Position rate (%) through Position rate (%) 1 23.53 3.80 14.94 7 2.79 3 11.19 2.11 4 7.47 1.57 5.29 10 1.18