Further Maths revision

A key feature of a perpetuity is that:

• The interest paid is higher than an annuity.

• There are no fees charged.

• The amount in the bank remains constant.

• The interest rate always increases over time.

• The interest rate always decreases over time.

The association between two variables y and

x, as shown in the scatterplot, is non-linear. In an attempt to transform the relationship to linearity, a student would be advised to:

• leave out the first four points

• use a y^2 transformation

• use a log(y) transformation

• use a 1/y transformation

• use a least squares regression line

What does a residual plot tell us?

• The strength of the linear association between the variables

• The impact that change in the explanatory variable has on the response variable

• The predicted values of the response variable

• The difference between the actual data value and predicted data value

• The impact that change in the response variable has on the explanatory variable

What conclusion can we draw from the residual plot shown?

• The original data is non-linear

• The original data is linear

• The data has no linear association

• There were many outliers

• The predicted values we generate

The regression line equation of transformed data is given as y= 50+ 4 × x^2

Calculate y if x = -3

• 14

• 86

• 43

• 38

• 0

What information is provided by the vertical axis intercept of a regression line?

• The change in the response variable for each unit increase in the explanatory variable.

• The change in the explanatory variable for each unit increase in the response variable.

• The reliability of the prediction.

• The strength of the linear association of the data.

• The value of the response variable when the explanatory variable equals 0.

A regression line has the equation debt= 0.75 - 7.3(age)

What is the expected change in debt for each unit increase in age?

• Increase of 0.75

• Decrease of 0.75

• Increase of 7.3

• Decrease of 7.3

• None of the above

The response variable is always located on

• the horizontal x-axis

• either axis; depends on what suits the data

• the vertical y-axis

• there usually isn't a response variable

A histogram has no spaces between columns and is a graphical way of displaying __________ data, whereas a bar chart has spaces between columns and is designed to display __________ data.

• categorical; numerical

• large set of; small sets of

• boring; interesting

• numerical; categorical

Calculate log₁₀ (456.2) correct to 3 significant figures.

• 2.659

• 2.65

• 2.66

• 3.00