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Question for thought: Would you always draw the same conclusion with the addition of an outlier?ħ. Including the outlier changes the evidence regarding a linear correlation. Including the outlier does not change the evidence regarding a linear correlation. Would inclusion of the outlier change the evidence for or against a significant linear correlation? What is the correlation coefficient without the outlier? What is the correlation coefficient with the outlier? The following bivariate data set contains an outlier.

What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place.Ħ. What is the correlation coefficient for this data set?įind the correlation coefficient and report it accurate to three decimal places. You then have Excel plot the trend line and report the equation and the r2 value.

Use this to predict the number of situps a person who watches 1.5 hours of TV can do (to one decimal place)

A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). Where MSE is the MSE of the linear regression model of y on x.1.ěased on the data shown below, calculate the correlation coefficient (to three decimal places)īased on the data shown below, calculate the regression line (each value to two decimal places)ģ. To estimate the mean and total of y-values, denoted as \(\mu\) and \(\tau\), one can use the linear relationship between y and known x-values. In addition, if multiple auxiliary variables have a linear relationship with y, multiple regression estimates may be appropriate. The two estimates, regression and ratio may be quite close in such cases and you can choose the one you want to use. This does not mean that the regression estimate cannot be used when the intercept is close to zero. When the auxiliary variable x is linearly related to y but does not pass through the origin, a linear regression estimator would be appropriate.

Looking at the data, how will we find things that will work, or which model should we use? These are key questions. The variance for the estimators will be an important indicator.