Transforming Data Quiz

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If I have a positive z-score, am I ABOVE or BELOW the mean?

• ABOVE

• BELOW

Suppose that the relationship between the amount of money (in $million) won by a tennis player ranked in the top 25 and their ranking can be modelled by the equation:  $winnings=0.491+5.767\times1/rank$  

 From this model we would predict that a player ranked at number 20 would win approximately:

• $0.313 million 

• $125 million

• $0.779 million 

• $116 million

•  $1.068 million

The association between the total weight of produce picked from a vegetable garden and its width is non-linear. An  $x^2$   transformation is used to linearise the data.When a least squares line is fitted to the data, its y-intercept is 10 and its slope is 55. Assuming that weight is the response variable, the equation of this line is:

•  $\left(weight\right)^2$  =10 + 5× width

•  width = 10 + 5 ×  $\left(weight\right)^2$  

• width = 5 + 10 ×  $\left(weight\right)^2$  

• weight = 10 + 5 × $\left(width\right)^2$  

•  $\left(weight\right)^2$  = 5 + 10 × weight

A regression line, found using a logx transformation is shown on the scatterplot. The line has an intercept of 47.7

and a slope of −13.9. Based on this information, the model which has been fitted to the data can be written as:

• time = 47.7 −13.9 × horsepower

• time = 47.7 −13.9 × log(horsepower)

• time = 13.9 +47.7 × log(horsepower)

• log(horsepower) = 47.7 −13.9 × time

• time = 47.7 +13.9 × log(horsepower)