Bivariate data review

Bivariate Data Review

7A Response and Explanatory Variables

• The explanatory variable (EV) is the variable that explains/predicts the value of the response variable. Also know as the independent varaible (IV)

• The response variable (RV) is the variable that responds to the change in the EV, Also known as the dependent variable (DV)

Multiple Choice

We wish to investigate the relationship between the number seeds planted in a garden and the number of fruit grown. The explanatory variable (EV) is

• The number of fruit grown

• The amount of soil in the garden

• The number of hours spent watering the plants

• The number of seeds planted

• None of the above

Multiple Choice

We wish to investigate the relationship between the time spent shopping and the number of items bought. The response variable (RV) is

• The number of items bought

• The number of items at the shop

• The time spent shopping

• The time spent getting to the shops

• None of the above

7B Constructing a Scatterplot manually

• The explanatory variable lies along the x-axis (x values from table)

• The response varibale lies along the y axis (y values from table)

7 C How to interpret a scatterplot

• Direction

• Form

• Strength

Direction of an association

• Positive association when the points move up as we go left to right

• Negative association when the points move down as we go left to right

• No association if there is no pattern

Form of an association

• Linear: When the points are scattered around a straight line

• Non-linear: When the points are scattered around a curved line

• 
  

Strength of an association

• Strong association : small amount of scatter in plot

• Moderate association: moderate amount of scatter in plot

• Weak association: large amount of scatter in plot

• No association: no pattern can be seen

Multiple Choice

The scatterplot shows the airspeed (in km/h) and the number of seats, of 16 commercial aircraft. Which of the following statements best match the scatterplot?

• There is no relationship between the airspeed of an aircraft and the number of seats.

• There is a strong negative linear relationship between the airspeed of an aircraft and the number of seats.

• There is a strong positive non-linear relationship between the airspeed of an aircraft and the number of seats.

• There is a strong positive linear relationship between the airspeed of an aircraft and the number of seats.

• There is a strong positive linear relationship between the airspeed of an aircraft and the number of seats, with one outlier.

7 D Pearson's correlation coefficient (r)

• Measures the strength of a linear relationship

• Has a value between -1 and +1

• Is positive if the direction of the linear relationship is positive

• Is negative if the direction of the linear relationship is negative

Correlation and causation

• Common response: where both measured variables are affected by a third AND different variable

• Confounding response: where the apparent effect of one variable is caused by a totally different variable

• Coincidence: where it is just by pure chance

• 
  

Multiple Choice

A correlation coefficient of 0.85 indicates that there is:

• no relationship between the variables involved.

• a weak negative relationship between the variables involved.

• a weak positive relationship between the variables involved.

• a moderate positive relationship between the variables involved

• a strong positive relationship between the variables involved.

7E Determining the value of Pearson's correlation coefficient, r

• Enter table into list and spreadsheets

• Press menu, 4, 1, 4

Coefficiency of determination

% of variation in RV is explained by EV. 100%-% is explained by other variables

7F Using the least squares line to model a linear association

• Least squares line is found by finding the values of the intercept and slope for that line that minimizes the sum of the squared residuals

7G Using a regression line to make predictions: interpolation and extrapolation

• Interpolation: predicting within the range of data

• Reasonable to expect the prediction is reliable when interpolating

• Extrapolation: predicting outside the range of data

• When extrapolating prediction may be unreliable

Multiple Choice

the following equation was created using a group of students whose height ranged between 163cm and 190cm

weight= -40 + 0.6 x height

Predicting the weight of someone who is 155cm is an example of

• Interpolating

• Extrapolating

7H Interpreting the slope and the intercept of a regression line

• the slope (b) predicts the change in the response variable (y) for each one-unit increase or decrease in the explanatory variable (x)

• the intercept (a) predicts the value of the response variable (y) when the explanatory variable (x) = 0