1. Using the paired height/pulse data for males, we get the regression equation: y^ = 73.9 + 0.0223x where x
represents height (cm) and the pulse rate is in beats per minute. a. What does the symbol y^ represent? b. For this example, which variable is the predictor variable and what does it represent? c. For this example, which variable is the response variable and what does it represent?
2. Weight (Ounces) Price (Dollars) 0.3 510 0.4 1151 0.5 1343 0.5 1410 1.0 5669 0.7 2277 a. Construct a scatter plot. What does the scatterplot suggest about a linear correlation between time and distance? b. Find the value of the linear correlation coefficient and determine whether there is sufficient evidence to support the claim of a linear correlation between weight and price of gold. Use a significance level of 0.05. c. Letting y represent the time and let x represent the distance, find the regression equation. d. Based on the given sample data, what is the best predicted price for a piece of gold that weighs 1.5 ounces?
3. You are given a correlation coefficient of r = 0.933 where x = weight of males and y = the waist size of males. Use the value of the correlation coefficient, r, to find the coefficient of determination and the percentage of total variation that can be explained & unexplained by the linear relationship. a. Find the coefficient of determination. What is the meaning of this value? b. What is the explained variation? What is the meaning of this value? c. What is the unexplained variation? What is the meaning of this value?
4. 4. Let the predictor variable x represent the heights (cm) of females and let the response variable y represent the weights (kg) of females. A sample of 40 heights and weights result in a standard error = 17.5436. a. What does the value of the standard error represent? b. The 95% prediction interval for this sample is (50.7, 123.0). Write statement that correctly interprets this prediction interval. c. A height of 180 cm is used to find that the predicted weight is 88.0 kg. What is the advantage of using a prediction interval for the results from the prediction interval instead of using the predicted weight of 88.0 kg?
5. An investigator analyzed the leading digits of the amounts from 200 checks issued by three suspect companies. The frequencies were found to be 68, 40, 18, 19, 8, 20, 6, 9, 12 and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford's law, the check amounts appear to be the result of fraud. Use a 0.05 significance level to test for goodness-of-fit with Benford's law. a. Calculate the χ2 test statistic. b. Calculate the χ2 critical value. c. Is there sufficient evidence to conclude that the checks are the result of fraud?
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