In Exercise 9.21, we see that the conditions are met for using the pH of a lake in Florida to predict the mercury level of fish in the lake. The data are given in FloridaLakes. Computer output is shown for the linear model with several values missing:

(a) Use the information in the ANOVA table to compute and interpret the value of R².
(b) Show how to estimate the standard deviation of the error term, s_Ñ”.
(c) Use the result from part (b) and the summary statistics below to compute the standard error of the slope, SE, for this model:

Exercise 9.21

The FloridaLakes dataset, introduced in Data 2.4, includes data on 53 lakes in Florida. Two of the variables recorded are pH (acidity of the lake water) and AvgMercury (average mercury level for a sample of fish from each lake). We wish to use the pH of the lake water (which is easy to measure) to predict average mercury levels in fish, which is harder to measure. A scatterplot of the data is shown in Figure 2.49(a) on page 106 and we see that the conditions for fitting a linear model are reasonably met. Computer output for the regression analysis is shown below.

Transcribed Image Text:

The regression equation is AvgMercury = 1.53 - 0.152 pH Predictor Coef SE Coef т 1.5309 Constant 0.2035 7.52 0.000 pH -0.15230 **(c)** -5.02 0.000 S= **(b)** R-Sq = **(a)** Analysis of Variance Source DF MS Regression 2.0024 2.0024 25.24 0.000 Residual Error 51 4.0455 0.0793 Total 52 6.0479 Mean StDev Minimum Maximum Variable pH AvgMercury 53 0.5272 0.3410 53 6.591 1.288 3.600 0.0400 9.100 1.3300