Maths: Test 2 Revision

Created by

Evelyn Allan

Cards (69)

Line of best fit
A straight line that represents the trend of the data
Correlation 
A measure of the association between numerical variables
When describing correlation both strength and direction should be considered
Line of best fit
A line done by eye
Line of Regression Formula
ŷ = ax+b
b 
y intercept
The regression line will always pass through the centroid of distribution
The better the fit of the line of regression 
The stronger the correlation between the two variables
The effect of outliers is significant
Slope 
For every increase of 1 unit in the explanatory variable, there is an average increase/decrease of the gradient unit in the response variable
intercept 
If the value of explanatory variable is 0 units, the predicted value of response variable is y intercept units
Coefficient of determination 
The variation in the response that is directly related to or explained by the variation in the explanatory variable. Tells us how well the regression line actually represents the data set
r^2 (percentage) of the variation in the response variable can be explained by variation in the explanatory variable
r^2 cannot be negative
Interpolation 
Predicting a value within the range of a given data set. Usually fairly reliable when there is a strong correlation between the variables
Extrapolation 
Predicting a value outside the range of the given data. Extrapolation fairly close to the range of data is fairly reliable if it is associated with a strong correlation between variables. Extrapolations any distance from the given data should be treated with caution
Outlier
A point of the data that differs from the overall value as indicated by a scatterplot and has a large residual value
Residual value 
The observed value - the predicted value = y-ŷ
A residual plot is used to determine if linear regression is appropriate for prediction purposes
If the residual plot is random - linear regression is appropriate
If the residual plot shows a non random placement of dots - linear regression is not appropriate
Line of best fit 
A straight line that represents the trend of the data
Correlation 
A measure of the association between numerical variables
When describing correlation both strength and direction should be considered
Line of best fit
A line done by eye
Line of Regression Formula
ŷ = ax+b
b 
y intercept
The regression line will always pass through the centroid of distribution
The better the fit of the line of regression 
The stronger the correlation between the two variables
The effect of outliers is significant
Slope 
For every increase of 1 unit in the explanatory variable, there is an average increase/decrease of the gradient unit in the response variable
intercept 
If the value of explanatory variable is 0 units, the predicted value of response variable is y intercept units
Coefficient of determination 
The variation in the response that is directly related to or explained by the variation in the explanatory variable. Tells us how well the regression line actually represents the data set
r^2 (percentage) of the variation in the response variable can be explained by variation in the explanatory variable
r^2 cannot be negative
Interpolation 
Predicting a value within the range of a given data set. Usually fairly reliable when there is a strong correlation between the variables
Extrapolation 
Predicting a value outside the range of the given data. Extrapolation fairly close to the range of data is fairly reliable if it is associated with a strong correlation between variables. Extrapolations any distance from the given data should be treated with caution
Outlier 
A point of the data that differs from the overall value as indicated by a scatterplot and has a large residual value
Residual value 
The observed value - the predicted value = y-ŷ
A residual plot is used to determine if linear regression is appropriate for prediction purposes