Correlation, Regression and Hypothesis Testing

Question 1

What is the Product Moment Correlation Coefficient (PMCC) and what is its symbol?

Answer 1

A measure of the strength of a correlation and what type it is (positive / negative).
Symbol is r

Question 2

What value of r would describe a perfect negative correlation?

Answer 2

-1

Question 3

What value of r would describe a perfect positive correlation?

Answer 3

1

Question 4

Between what range would a correlation generally be considered ‘weak’?

Answer 4

-0.2 & 0.2

Question 5

Between what range would a correlation generally be considered ‘strong’?

Answer 5

+/- 0.75 & 1

Question 6

How do you use your calculator to find the regression line and pmcc (r)?

Answer 6

• Turn frequency off (shift setup statistics)
• Select statistics mode (6)
• Select y = a + bx
• Enter data
• Press OPTN and select Regression Calc

Question 7

What is interpolation?

Answer 7

Using the line of best fit to make predictions for data that lies within the range of observed data.

Question 8

What is extrapolation?

Answer 8

Using the line of best fit to make predictions for data that lies outside of the range of observed data ( extending the line of best fit beyond data)

Question 9

Why is extrapolation often not useful for predicting values?

Answer 9

Relies on the assumption that the trend will continue outside of the range which may not hold true in all scenarios

Question 10

What is a causal correlation?

Answer 10

When a change in one variable directly affects the other. Some relationships may be correlated but may not be directly the cause of the other (there is a correlation between rates of diabetes and annual income in some groups but this is because they both relate to dietary intake)

Question 11

What are correlations without a causal connection known as?

Answer 11

Spurious correlations

Question 12

What is a regression line?

Answer 12

A line of best fit for a correlation
( in form y = mx + c )

Question 13

What is the constant C term in a regression line?

Answer 13

When x is zero units, C is the predicted number of y

Question 14

What is the m gradient term in a regression line?

Answer 14

For every increase in x by 1 unit, there must be an increase/decrease in y by m units

Question 15

How do you create a straight line from a polynomial in form y = axⁿ?

Answer 15

• log(y) = log(axⁿ)
• log(y) = log(a) + log(xⁿ)
• log(y) = log(a) + nlog(x)
  Compare to y = mx + c
  log(y) = y, log(x) = x, n = m, log(a) = c

Question 16

How do you create a straight line from an exponential in form y = kb^x?

Answer 16

• log(y) = log(kbⁿ)
• log(y) = log(k) + log(b^x)
• log(y) = log(k) + xlog(b)
• Compare to y = mx + c
• log(y) = y, x = m, log(k) = c

Question 17

What is a in the equation y = ab^t?

Answer 17

The initial value of the variable y

Question 18

What is b in the equation y = ab^t?

Answer 18

The proportional increase/decrease in the number of y for 1 time period

Question 19

Where do you find probabilities for hypothesis testing, in order to calculate where the critical region lies?

Answer 19

In the formula booklet (page 37)