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Chapter 7 - Bivariate data - Coggle Diagram
Chapter 7 - Bivariate data
7A - Bivariate data
The relationship between two variables
The explanatory variable - Explains or predicts the value of the response variable (IV) (x-axis)
The response variable - (DV) (y-axis)
7B - Scatterplots
A visual display of the relationship between two numerical variables.
Each point represents s single case. Try to be as accurate and neat as possible.
CAS
7C - Interpreting scatterplots
Having established a relationship exists we look for certain features.
Direction (positive or negative)
Form (Linear, non liner (if any))
Strength (strong, moderate, weak)
7D - Pearson's correlation coefficient
Assumptions
The data is numerical
The association is linear
Properties
Has a value between -1 and 1
If its a positive slope the number is positive, negative slope the number is negative
Correlation /= causation
Both variables could be affected by a third variable (common)
Both variables are effected by a number of other variables (confounding)
It might be pure chance that the variables appear to be related (coincidence)
7F - Least Squares regression line
The line of best fit (LSR - least squares regression) is a line that best fits your data
Residual = The vertical distance between a data point and the LSR
The residual(s) = the smallest distance between the data point and line
(Must assume the data is numerical and have a linear association)
Significant figures
After a decimal point, all zeroes at the end of the number are significant
All zeros between significant figures are significant
All non-zero digits are significant
7G + H - Making Predictions
Make predictions by substituting a number into the linear regression line equation
Interpolation = Predicting within out range of data so should be reliable (before the last data point)
Extrapolation = Predicting outside our range of data, no way to know if the data continues in the same way therefore is not reliable (after the last data point)
Interpret = writ a statement about what they each show.
Slope = Predicts the change in the response for each increase or decrease in the explanatory variable.
Intercept = Predicts the value of the response variable when the explanatory variable (x) equals zero