Maths: Test 2 Revision

• 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
• 1. 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
• 1. 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