A group of chemical engineers are trying to determine the cost of refining a mixture based on the concentration of a particular chemical. After refining 50 samples of the mixture and recording the cost they fit a simple linear regression model to the data. Partial computer output is given below. Predictor Constant Coef SE Coef T P 2.51 0.563 4.45 <0.0001 Concentration 2.55 0.980 2.61 0.0122 A scatterplot of cost versus concentration had a moderately, strong curved relationship. Based on these results, what conclusion can be drawn from this analysis at the 5% significance level? (A) There is evidence of a significant positive linear relationship between concentration and cost. (B) There is evidence of a significant negative linear relationship between concentration and cost. (C) There is evidence of a significant linear relationship between concentration and cost but the direction is unknown. (D) There is evidence of a significant non-linear relationship between concentration and cost. (E) The analysis is inconclusive because the assumptions for the linear regression 1-test are not met.

Olympic 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?

What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?

A b c