X e the standard deviation of the responses is the

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x E: The standard deviation of the responses is the equal at each value of x . These conditions are checked by examining the residual plots: residuals vs. explanatory variable and histogram/normal probability plot of the residuals. The Analyzing Two Quantitative Variables applet, Minitab ( Stat > Regression > Regression > Fit Regression Model ), and R ( >summary(lm(response~explanatory) all automatically report the two-sided p-value. This p-value can be divided in half to obtain a one-sided p-value (assuming the observed slope is in the direction conjectured). Discussion : Typically we are most interested in testing whether the population slope coefficient equals zero, as that would suggest that the population regression line is flat and so the explanatory variable is of no use in predicting the response variable. Because testing whether the slope coefficient is zero tests whether the regression model with this explanatory variable is of any use, it is sometimes called a model utility test .
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Chance/Rossman, 2015 ISCAM III Exploration 401 There are situations where we might want to test other values of the population slope, for example E 1 = 1 (do x and y change at the same rate?). We can also use the same approach to carry out tests and create confidence intervals for the population intercept. However, these are less useful in practice, in particular because the intercept is often far outside the range of data and does not have a meaningful interpretation. Checking the technical conditions is an important step of the process. Notice that you will typically fit the regression model first to obtain the residuals to allow you to assess the model. As with ANOVA, these t procedures are fairly robust to departures from normality. If the conditions are violated, you can again explore transformations of the data. Technology Exploration: The Regression Effect In the 2013 Masters golf tournament, Spaniard Sergio Garcia had a score of 66 in the first round but a score of 76 in the second round. Keep in mind that in golf, lower scores are better than higher scores. Is this evidence that he choked? The data file Masters13.txt contains golfers’ scores in the first two rounds of the 2013 Masters. (a) Use technology to construct a scatterplot of second round score vs. first round score. Also calculate the correlation between these two. Does it reveal an association between scores in these two rounds? If so, is it positive or negative? Would you call it weak, moderate, or strong? (b) Use technology to sort the data according to the golfers’ first -round scores: x In R > mydata=data.frame(golfer, round1, round2) > sortdata=mydata[order(mydata[,2]),] x In Minitab MTB> sort c1-c3 c5-c7; SUBC> by c2. Or Choose Data > Sort , entering movie, score, and rating in the Sort columns box and score in the By column box.
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