VCE Further Maths Ch5 Transformations Review

The missing data values, a and b, in the table above are:

• a = 1.477, b = 400

• a = 1.301, b = 900

• a = 0.05, b = 900

• a = 900, b = 1.301

• a = 900, b = 2.996

Select the statement which correctly completes the sentence “The effect of a squared transformation is to …”

• stretch the high values in the data

• maintain the distance between values

• stretch the low values in the data

• compress the high values in the data

• maintain the order of the values in the data

The relationship between two variables y and x as shown in the scatterplot is non-linear. Which of the following transformations is most likely to linearise the relationship?

• an $x^2$ transformation

• a log y transformation

• a $y^2$ transformation

• a 1/y transformation

• none of the above

The relationship between two variables y and x as shown in the scatterplot is non-linear. Which of the following transformations is most likely to linearise the relationship?

• an $x^2$ transformation

• a log y transformation

• a log x transformation

• a 1/y transformation

• none of these

A log (y) transformation is applied to the data above, and a least squares regression line fitted to the transformed data set. The equation of the least squares regression line is given by:

• log y = 71.313 – 16.567x

• log y = 0.374 – 1.981x

• log y = 1.981 – 0.374x

• log y = 5.264 – 2.643x

• log y = 2.643 – 5.264x

 Suppose that the model which describes the relationship between the literacy rate of a country and the GDP of that country can be modelled by the equation:
literacy rate = –40 + 30log(GDP) 

From this model we would predict that a country with a GDP of $20 000 would have a literacy rate of:

• 89%

• 43%

• 257%

• 99%

• 87%

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)

The objective of transforming data is:

• Create a scatterplot

• Smooth the data

• Create a residual plot

• Linearise the data

• Drain my life