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quiz_02_23feb2011_solution

# quiz_02_23feb2011_solution - Name Assigned TF and Section...

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Name: Assigned TF and Section time: Statistics 100 Quiz 2 Wednesday 23 February 2011 This quiz has five questions and is worth 25 points; four of the questions are on the second page. The scatterplot below shows the relationship between driver age (in years) and the maximum distance at which a highway sign is legible (in feet). The summary statistics for the variables age and distance are given below the plot. 300 400 500 600 Distance 20 40 60 80 Age Variable | Obs Mean Std. Dev. -------------+----------------------------- age | 30 51.0 21.78 distance | 30 423.3 81.72 correlation age distance = -0.80 1. What is the equation of the least squares regression line for these data? From the table above we have s y = 81 . 72 , s x = 21 . 78, and the correlation r = - 0 . 80. Thus, we can find the slope by substituting these values in: b 1 = r · s y s x = ( - 0 . 80) × 81 . 72 21 . 78 = - 3 . 002 Also from the table, ¯ y = 423 . 3 , ¯ x = 51 and so the y –intercept is given by: b 0 = ¯ y - b 1 ¯ x = 423 . 3 - ( - 3 . 002)(51) = 576 . 402 So the equation of the least squares regression line is given by: y = 576 . 402 - 3 . 002 x .

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quiz_02_23feb2011_solution - Name Assigned TF and Section...

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