Variables
Interpreting a Scatterplot
Pearson's correlation coefficient
Interpreting and predicting from a linear model
Random
100
What is the explanatory variable (EV)?
EV is the variable we expect to explain or predict the value of the another variable.
100
When interpreting scatterplots, what features we mainly discuss about?
Direction, Strength and Form.
100
The symbol we use to represent Pearson's correlation coefficient is _____.
The letter r.
100
Which regression line is the best model of the data? and why?
Line 1. The most fitting regression line should follow the trend of the data points and be in close proximity to all of them.
100
How to calculate the correlation coefficient (r) with CAS Spreadsheet? Please read out each step you pressed.
Menu
4. Statistics
1. Stat Calculations
4. Linear regression line (a + bx)
200
What is the response variable (RV)?
RV is the expected effect, and it responds to explanatory variables (EV).
200
How many different type of form of scatterplots? What are they?
There 2 types of form, which are Linear amd Non-linear.
200
The r value is positive, the linear relationship is...
Positive.
200
Describe a real world relationship that would have a strong positive association.
Possible answer: As number of hours studied increase, test scores would increase.y = 4x
200
Which of the following are Numerical Variable?
The number of pages in a book.
Kindergarten pupils' favourite toys.
The volume of petrol (in litres) used to fill the tank of a car.
The language(s) that you have studied.
The number of pages in a book & The volume of petrol (in litres) used to fill the tank of a car.
300
Data is collected to investigate the association between age of a second-hand textbook and its selling price. The Response Variable is...
The selling price.
300
How we describe the strength of a scatterplot?
We describe it with Weak/Moderate/Strong.
300
Pearson's correlation coefficient measures...
The strength of a linear association.
300
Write the equation for the trend line shown in the scatter plot below, using the two points (0,453) and (10,359).
y=-9.4x+453
300
True or False:
Correlations doesn't mean causation.
Why, please expain.
True. There may be other factors that are able to influence the Response Variable, i.e, there is not a one-to-one only correlation between EV and RV.
400
A person's height predicted from their wrist circumference. The explanatory variable is...
The wrist circumference.
400
The association of two variables is ________________ when EV increases RV increases.
Positive
400
The range of values for Pearson's correlation coefficient is _______________.
-1 to 1.
400
Interpret the slope for the following
Son's height (cm)= 0.54 × Father's height (cm) +89.58
On average, for every 1cm increase in father's height, there is a 0.54 increase in son's height.
400
Students sit for two exams, two weeks apart. The following regression equation can be used to predict the students’ marks on exam 2 from the marks they obtained on exam 1.
mark on exam 2 = 15.7 + 0.650 × mark on exam 1
Use the equation to predict the mark on exam 2 for a student who obtains a mark of 20 on exam 1. Give your answer to the nearest mark.
Mark on exam 1 = 20
Mark on exam 2 = 15.7 + 0.650 × 20 = 28.7
Round to the nearest mark means give you anser as a whole number, which is 29 marks.
500
A scatterplot is a plot which enables us to display bivariate data when both of the variables are _______________.
Numerical.
500
The association of two variables is _______________ when EV increases and RV decreases.
Negative
500
When value of correlation coefficient (r) of a pair of variables is close to zero, that means there is _____________ association/relationship between the two variables.
No association.
500
Interpret the y-intercept for the following:
Son's height (cm)= 0.54 × Father's height (cm) +89.58
Please discuss whether this is possible and give your thoughts/reasons. What do we call the EV in such situation/range?
On average, when father's height is zero, son's height is 89.58cm.
It's impossible, because every child born has a biological father and cannot be 0 cm tall.
We all the EV which is outside the range as Extrapolation.
500
Please rewrite the following statement if you think it's inappropraite.
‘As the smoking rate increases then the incidence of heart disease will also increase.’
Pssible answer:
Countries with high incidents of smoking will have high rates of heart disease.