Question

Dr. Lilian Fok, a New Orleans psychologist, specializes in treating patients who are agoraphobic (ie, afraid to leave their homes). The following table indicates how many patients Dr. Fok has seen each year for the past 10 years. It also indicates what the robbery rate was in New Orleans during the same year. Year 10 Number of Patients 36 32 39 42 42 5660545760 Robbery Rate per 1,000 Population 583 611 73.0 757 815 890 996 942 1032 1172 The simple linear regression equation that shows the best relationship between the number of patients and year is (round your responses to three decimal places). where y Dependent Variable and x Independent Variable

a) The simple linear regression equation that shows the best relationship between the number of patients and year is (round your responses to three decimal places).

y= _ + _x

b) Using linear regression the number of patients Dr. Fok will see in year 11 = _____ patients (round your response to two decimal places).

c) Using linear regression, the number of patients Dr. Fok will see in year 12 = _____ patients. (round your response to two decimal places).

Answer 1

a) Simple linear regression equation is determined using least square method as follows:

Simple Linear Regression (Least Squares Regression Method 36 36 32 64 39 9 42 168 16 42 210 25 56 6 336 36 420 49 60 54 432 64 513 57 9 81 10 100 60 600 478 385 2896 255 Regression Equation: y a bx, where x Year (Independent variable) y = Number of patients (dependent variable) a intercept point of regression line and y-axis b-slope of regression line 385 10 (Ex- 3025 478 2896 Ny- 3.236 N 2x - (Ex) Slope (b) Intercept (a)- Regression Equation: y : 30 + 3.236x

y = 30 + 3.236*x

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b) For year 11, x = 11, Number of patients Dr. Fok will see y = 30 + 3.236*11 = 65.60 patients

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c) For year 12, x = 12, Number of patients Dr. Fok will see y = 30 + 3.236*12 = 68.83 patients