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# LectureChapter4.pdf MATH-10041-002

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This 2 page Class Notes was uploaded by Amy Turk on Saturday April 2, 2016. The Class Notes belongs to MATH-10041-002 at Kent State University taught by Dr. Joseph Minerovic in Spring 2016. Since its upload, it has received 33 views. For similar materials see Introductory Statistics in Math at Kent State University.

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Date Created: 04/02/16

Math Chapter 4 ● weak associations result in a large amount of scatter in the scatterplot ● the stronger the association, the better the model is for prediction ● variation is not important when studying scatterplots ● correlation coefficients can range from -1 to 1 ○ its not possible to have a correlation coefficient outside this range ● the correlation coefficient is a measure that describes the direction and strength of a linear relationship ○ can be used for two quantitative variables only ● a correlation coefficient of zero indicates that there is no linear relationship between the two quantitative variables ● the mean of the data set is often the best estimate of the parameter ○ the best estimate is also the best prediction ● regression is used to find the equation that best fits the data ○ it finds the equation that minimizes the error in the dependent variable for the given values of the predictor variable ● a regression line gives a linear equation relating the independent and dependent variable ○ allows predictions of the dependent variable to be made based on the value of the independent variable ○ gives us a better prediction than just the mean ● linear relationships are not curved ● the correlation coefficient remains the same when the numbers are multiplied by a positive constant ● the correlation coefficient remains the same when a constant is added to each number ● positive correlation means that both variables tend to increase or decrease together ● negative correlation means that two variables tend to change in opposite directions, with one increasing while the other decreases ● no correlation means that there is no apparent relationship between the two variables ● how we determine the strength of a correlation: the more closely two variables follow the general trend, the stronger the correlation, which may be positive or negative ● the correlation coefficient is a number that measure the strength of the linear association between two numerical variables ○ represented by r ○ always a number between -1 and 1 ● the correlation coefficient makes sense only if the trend is linear and the variables are numerical ● a correlation coefficient based on observational study can never be used to support a claim of cause and effect ● when computing a correlation coefficient, changing the order of the variables does not change r ○ in an equation, it does not matter which variable is called x and which is called y ● if there is no trend, the value of r is near zero ● the regression equation is a tool for making predictions about future observed values. It also provides a useful way of summarizing a linear relationship ● statisticians often write the word “predicted” in front of the y-variable in the equation of the regression line to emphasize that the line consists of predictions for the y-variable, not actual values ● another name for the regression line is the least squares line ● regression lines make predictions about the values of y for a given x-value ● an influential point is a point that changes the regression equation by a large amount ● correlation does not imply causation ○ just because two variables are related does not show that one caused the other ● extrapolation means that the regression line is used to make predictions beyond the range of the data ● regression towards the mean = if a variable is extreme on its first measurement, it will tend to be closer to the average on a second measurement ○ if it is extreme on the second, it will tend to have been closer to the average on the first ● regression models are useful only for linear associations ● outliers = influential points ● extrapolation = attempting to use the regression equation to make predictions beyond the range of data ● coefficient of determination = the value that measure how much variation in the response variable is explained by the explanatory variable ○ r squared = correlation coefficient squared

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