Unit 4 Section 4 Exercises MY ANSWERS (1)

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Jan 9, 2024

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Elementary Statistics Unit 4 : Section 4 Exercises Your solutions should be clear, complete, and sufficiently detailed in order to demonstrate your understanding and communicate your reasoning and method of solving the problem. Exercise 1 The height (in feet) and trunk circumference (in inches) at breast height (4.5 feet above the ground) was measured for a random sample of Eucalyptus trees. The data are summarized below. Trunk Circumference 21.1 20.8 22.5 19.4 23.6 19.8 21.6 19.9 Tree Height 34.2 32.7 35.0 31.9 36.5 31.2 33.8 31.4 (a) Determine the linear regression model that will best predict the height of a Eucalyptus tree based on its trunk circumference at breast height. (b) How well does the linear regression model fit this sample data? (c) Predict the height of a Eucalyptus tree with a trunk circumference at breast height of 22 inches. Page 1 Mathematics 13 L1 (xi) = TRUNK CIRCUMFERENCE L2 (yi) = TREE HEIGHT LinReg(ax+b) L1,L2 ON CALCULATOR GIVES US ANSWER: The linear regression model is yˆ = 1.250x + 6.989 r2= 0.928 Yes, the linear regression model fits the sample well because the coefficitent of determination r2 = 0.928 is quite close to 1. For x = 22, yˆ = 1.250 x (22) + 6.989 = 34.49 This means, the predicted height of a eucalyptus tree with a trunk circumference at breast height of 22 inches would be about 34.5 feet tall.

Elementary Statistics Unit 4 : Section 4 Exercises Exercise 2 A medical researcher wishes to determine how the dosage (in milliliters) of an experimental drug affects the heart rate (in beats per minute) of patients with an elevated heart rate. The data for a sample of eight patients with an elevated heart rate are provided in the following table. Drug Dosage 0 5 10 20 25 30 40 50 Heart Rate 135 124 106 89 85 72 68 62 (a) Determine the linear regression model that will best predict a patient’s heart rate based on the dosage of the drug received. (b) How well does the linear regression model fit this sample data? (c) If a patient with an elevated heart rate is administered a 35 ml dose of this drug, predict the resulting heart rate of the patient. Page 2 Mathematics 13 L1 (xi) = DRUG DOSAGE L2 (yi) = HEART RATE LinReg(ax+b) L1,L2 ON CALCULATOR GIVES US ANSWER: The linear regression model is yˆ = -1.48x + 125.92 r2= 0.920 Yes, the linear regression model fits the sample well because the coefficient of determination r2 = 0.920 is quite close to 1. For x = 35, yˆ = -1.48 x (35) + 125.92 = 74.1 This means, if a patient with an elevated heart rate is administered a 35 ml dose of this drug, the predicted resulting heart rate of this particular patient would be predicted to be around 74 BPM (beats per minute).

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