CALCULATING STANDARD DEVIATION WORKSHEET



Name: November 9th 2015Stats 1Stats.27 - Notes and PracticeLinear RegressionBefore attempting to fit a linear model to observed data, a statistician should first determine whether or not there is a relationship between the variables of interest. This does not necessarily imply that one variable?causes?the other (for example, higher SAT scores do not?cause?higher college grades), but that there is some significant association between the two variables. A?scatterplot?can be a helpful tool in determining the strength of the relationship between two variables. If there appears to be no association between the proposed explanatory and response variables (i.e., the scatterplot does not indicate any increasing or decreasing trends), then fitting a linear regression model to the data probably will not provide a useful model. A valuable numerical measure of association between two variables is the?correlation coefficient, which is a value between -1 and 1 indicating the strength of the association of the observed data for the two variables.Linear regression is about modeling the relationship between two variables by fitting a linear equation to observed data. One variable is considered to be an explanatory variable, and the other is considered to be a response variable. A linear regression line has an equation of the form:?y= a + bx x?is the explanatory variable and?y?is the predicted values of the response variable. ?b is the slope of the linea?is the y-intercept (the value of?y when?x= 0).The most common method for fitting a regression line is the method of least-squares. This method calculates the best-fitting line for the observed data by minimizing the sum of the squares of the vertical deviations from each data point to the line (if a point lies on the fitted line exactly, then its vertical deviation is 0). Properties of the Regression LineThe line minimizes the sum of squared differences between observed values (the?y?values) and predicted values (the ? values as computed from the regression equation).The regression line passes through the mean of the?X?values (x) and through the mean of the?Y values (y).The regression constant (a) is the y-intercept of the regression line.The regression coefficient (b) is the average change in the dependent variable (Y) for a 1-unit increase in the independent variable (X). It is the?slope?of the regression line.440055019049900Ti-84 Skills Enter data into ListsSTAT 1:Edit… enter values in L1 and L2 Graph Data (from lists) on a scatter plot2nd STAT PLOT 1:Plot1…Off Enter select “On” Enter29337008890000495300571500Adjust the graph view to fit data43338757366000ZOOM 9:ZoomStat Enter Calculate least-squares regression lineSTAT CALC 8:LinReg(a+bx) Calculate42767251270000Graph using equation of the linear regression line Y= enter a+bx on the first line (using values found for a and b) GRAPH4000501816100039319201968500Use your calculator’s Statistics functions to calculate the least-squares regression line and to show a scatter plot of each data set with the regression line!X081921167243129Y9121719151129405025615905334000Regression line______________________Regression constant: _______Regression coefficient: ________What would you expect the value of y to be when x has each of the values below?xy=a+bx1640100Use your calculator’s Statistics functions to calculate the least-squares regression line and to show a scatter plot of each data set with the regression line!X159935946475408387Y1,0324387617875949899234219825615905334000Regression line______________________Regression constant: _______Regression coefficient: ________What would you expect the value of y to be when x has each of the values below?xy=a+bx050150 ................
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