Statistics 121 notes week 4
Statistics 121 notes week 4 STAT 121
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This 3 page Class Notes was uploaded by Sydney Clark on Friday September 23, 2016. The Class Notes belongs to STAT 121 at Brigham Young University taught by Dr. Christopher Reese in Winter 2016. Since its upload, it has received 2 views.
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Date Created: 09/23/16
Stats 121 notes week 4 *IMPORTANT* *SAMPLE QUIZ QUESTIONS* Intro to Linear Regression o Correlation: Onenumber summary gives strength and direction of linear relationship o Correlation: Does NOT indicate location or steepness of linear relationship o Regression Summarizes linear pattern of scatterplot using “bestfitting” straight line Requires that one variable be as explanatory and the other as response. o Statistical model Mathematical expression for mean that relates response to explanatory Allows for variation in response Mean of y is a straight line function of x What ability does regression give you that correlation does not? (y = resp., x = expl.) (a) calculate x given y (b) calculate mean of x given y (c) calculate y given x (d) calculate mean of y given x o Examples mean systolic blood pressure as straight line function of age • mean income for bank tellers as straight line function of number of years in school mean profit as straight line function of minutes of advertising o Regression notation yˆ=a+bx where: A=intercept B=slope yˆ=predicted yvalue (mean of y for given x) o Regression line Also called best fitting line, least squares line, least squares regression line Line for which sum of squared vertical deviations of dots from line is minimized Vertical deviation= the difference between the observed y and the predicted y (also known as Residuals or prediction error) o Residuals o o If actual number is larger than predicted number the outcome is positive o Simple formulas for slope and intercept Y^=a+bx B= r Sy/Sx A=Y barbX bar o Interpretatin of slope b Change in the mean of y when x increases by 1 unit Mean height of sons increases by abour .61 inc for every 1 inch increase in the heights of fathers o Interpretation of intercept a Technically, mean of y when x is 0—anchors line in place, but not always meaningful. Mean height of sons predicted to be 25.68 inches when the height of fathers is 0 inches! o Interpretation of predicted y hat Mean of y when x equals a certain value Mean height of sons for fathers who are 70 inches tall is 25.68+.61(70) o VERY RARLEY IS “SLOPE” USED. THEY WRITE THE NAME OF THE X INTERECPT o Intercept is ‘a’ and slope is ‘b’ Correlation is an okay way to determine the strength of two variables but it doesn’t not have a good interpretation. Squared correlation (r^2) o R^2=% of the variability in y that is explained by the relationship between x and y o R^2 agrees with our i Variability= how spread out the points are Extrapolation: “extrapolation is bad” use of regression line to estimate mean of y for c far outside xrange of data o Problem: no information on nature of relationship outside xrange All relationships bend somewhere