Concept explainers
Regression between cereal sodium and sugar The following figure shows the result of a
a. What criterion is used in finding the line?
b. Can you draw a line that will result in a smaller sum of the squared residuals?
c. Now let’s look at a histogram of the residuals. Explain what the two short bars on the far right of the histogram mean in the context of the problem. Which two brands of cereal do they represent? Can you find them on the
d. In general, how reliable would you say amount of sugar is as a predictor of the amount of sodium?
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Statistics: The Art and Science of Learning from Data (4th Edition)
- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardNoise and Intelligibility Audiologists study the intelligibility of spoken sentences under different noise levels. Intelligibility, the MRT score, is measured as the percent of a spoken sentence that the listener can decipher at a cesl4ain noise level in decibels (dB). The table shows the results of one such test. (a) Make a scatter plot of the data. (b) Find and graph the regression line. (c) Find the correlation coefficient. Is a linear model appropriate? (d) Use the linear model in put (b) to estimate the intelligibility of a sentence at a 94-dB noise level.arrow_forwardOlympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forward
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