Math 133: 4.3 Worksheet #2 Coursepack, p. 537 Name: Section #: 4.3: Least-Squares Regression 1. The following data set gives the length and girth (both in centimeters) of a random sample of 12 harbor seals x = Length (cm) | y= Girth (cm) Find the following (Give 3 decimal place) 137 106 a) Correlation Coefficient: 168 130 152 116 b) Linear Regression Equation: 145 106 c) Describe the strength and direction of the relationship 159 125 between the data: (Circle one) 159 119 Strong Positive Moderate Positive Weak Positive 124 103 Strong Negative Moderate Negative Weak Negative 137 104 d) Coefficient of Determination: 155 120 148 110 e) Interpret the coefficient of determination in the context of the situation: 147 107 146 109 f) What is the slope of the regression equation? Interpret this value in the context of the situation. Be specific. g) What is the y-intercept of the regression equation? Interpret this value in the context of the situation or if it does not make sense, explain why. h) Find y if x = 148 using the linear regression equation. Interpret this value in the context of the situation.MAT 133: 4.3 WS 2 p.2 2. A large number of studies were analyzed to judge whether the length of time an employee has been at a job (called "tenure") has a correlation with their commitment to the company/job performance. The table below shows some results from a few of the studies. Average Tenure, Average Age, Pearson Correlation, and Sample Size for Each Study Sample Study Number Average tenure Average age years (years) 1. 2.5 n 28.4 0.62 2 . 4.0 85 23.5 3 . 0.45 1.2 25.0 112 0.35 4 . 3.7 59 30.5 .34 5. 2.5 171 23.8 0.26 55 Find the following: Use the study number (1, 2, 3, 4, 5) for b-e a) How many people were in Study #5? b) Which study had the oldest group of employees? c) Which study had the group with the longest tenure at their company? d) Which study had the lowest coefficient of determination? e) Which study showed the strongest relationship between tenure and commitment to the company/job performance? _ Explain how you can tell. 3. Circle which of the following represents the strongest relationship between two variables. r = 0.56 r = 0.43 r = 0.20 r = 0.14 r =- 0.69 4. Circle which of the following represents the weakest relationship between two variables. r = 0.56 r = 0. 43 r = 0.20 r = 0.14 r =- 0.69 5. True or False: If False, explain why. a) If the correlation coefficient between two variables is negative, that means that the slope of the regression line between those variables will be negative. b) A point that is an outlier in a scatter diagram will be an influential observation