The table below contains the pH measurement and mercury level amounts for 10 Florida lakes. pH | Mercury Level 7.3 | 0.27 5.4 | 0.48 8.1 | 0.19 5.8 | 0.83 6.4 | 0.81 5.4 | 0.71 7.2 | 0.5 7.2 | 0.49 5.8 | 1.16 7.6 | 0.05 a. Calculate and interpret the correlation coefficient. b. Find the equation of the least-squares regression line. c. Predict the mercury level for a lake that has a pH of 6.0.
Added by Benjamin M.
Step 1
To calculate the correlation coefficient, we first need to find the mean of both pH and mercury levels, and then use the formula for the correlation coefficient: $r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - Show more…
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Florida has over 7700 lakes. We wish to estimate the correlation between the pH levels of all Florida lakes and the mercury levels of fish in the lakes. It is found that the correlation between these two variables for a sample of size n=53 of the lakes is -0.575. (a) Give the notation for the quantity we are estimating. (b) Give the notation for the quantity we use to make the estimate. (c) Give the value of the best estimate. Round your answer to three decimal places.
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Florida Lakes Florida has over 7700 lakes. $^{12}$ We wish to estimate the correlation between the pH levels of all Florida lakes and the mercury levels of fish in the lakes. We see in Data 2.4 on page 71 that the correlation between these two variables for a sample of $n=53$ of the lakes is -0.575 . (a) Give notation for the quantity we are estimating, notation for the quantity we use to make the estimate, and the value of the best estimate. (b) Why is an estimate necessary here? What would we have to do to calculate the exact value of the quantity we are estimating?
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