Exam 10: Correlation and Regression

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 If the correlation coefficient r is equal to 0.566, find the coefficient of determination. \text { If the correlation coefficient } r \text { is equal to } 0.566 , \text { find the coefficient of determination. }

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A

In a study of reaction times, the time to respond to a visual stimulus (x)( x ) and the time to respond to an auditory stimulus (y)( y ) were recorded for each of 8 subjects. Times were measured in thousandths of a second. The results are presented in the following table. Visual Auditory 218 209 153 150 240 226 202 196 243 225 165 161 207 196 209 198 Compute the least-squares regression line for predicting auditory response time (y)( y ) from visual response time (x)( x ) .

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B

Total number of assists and the total number of points or a sample of NHL scoring leader: shown. Assists x Total Points y 26 48 29 68 32 66 34 69 36 76 37 67 40 84 Predict the total points if x=30x = 30 assists.

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 A formula for the correlation coefficient r is \text { A formula for the correlation coefficient } r \text { is } _____

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An architect wants to determine the relationship between the height (in feet) and nn of stories in a building. The data for a sample of 10 buildings in Pittsburgh are sh a. Draw the scatter plot for the variables. b. Give a brief explanation of the type of relationship. Stories x Height y 64 841 54 725 40 635 31 616 45 615 38 582 42 535 41 520 37 511 40 485

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In a study of reaction times, the time to respond to a visual stimulus (x)( x ) and the time to respond to an auditory stimulus (y)( y ) were recorded for each of 6 subjects. Times were measured in thousandths of a second. The results are presented in the following table. The following MINITAB output describes the fit of a linear model to these data. Assume assumptions of the linear model are satisfied. The regression equation is Auditory =240.686515+0.109829= 240.686515 + 0.109829 Visual Predictor Coef SE Coef T P Constant 240.686515 14.271226 16.865161 0.000073 Visual 0.109829 0.066275 1.657159 0.172829 What is the intercept of the least-squares regression line?

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 If the correlation coefficient r is equal to 0.526, find the coefficient of nondetermination. \text { If the correlation coefficient } r \text { is equal to } 0.526 \text {, find the coefficient of nondetermination. }

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The standard error of estimate can be used for constructing a(n) __________interval about a yy ^ { \prime } value.

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Daniel Wiseman, a scientist for Gres-Trans Corp., wants to determine if the flow rate of a particular material changes with different changes in temperature. The data is plotted in tl below. What type of relationship exists between the flow rate and the change in temperatı Daniel Wiseman, a scientist for Gres-Trans Corp., wants to determine if the flow rate of a particular material changes with different changes in temperature. The data is plotted in tl below. What type of relationship exists between the flow rate and the change in temperatı

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The range of the correlation coefficient is from 0 to 1.

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A correlation coefficient of 0.9610.961 would mean that the values of xx increase as the values of yy decrease.

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If there is a strong negative linear relationship between the variables, the value of will be close to -1.

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is a statistical method used to determine whether a relationship between variables exists.

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What is the value of yy ^ { \prime } when x=3x = 3 , if the equation of the regression line is y=23.13.8xy ^ { \prime } = 23.1 - 3.8 x ?

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In a relationship, as one variable increases, the other variable decreases, and vice versa.

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Compute the standard error of the estimate for the data below. Round to the thousandths 1 x 27 28 29 30 31 32 y 116.95 120.37 125.26 124.90 129.37 130.90

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The two variables in a scatter plot are called the

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The director of an alumni association for a small college wants to determine whetl there is any type of relationship between the amount of an alumnus' contribution ( dollars) and the number of years the alumnus has been out of school. The data fol a. Draw the scatter plot for the variables. b. Give a brief explanation of the type of relationship. Years x Contribution y 1 500 5 100 3 300 10 50 7 75 6 80

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The standard error of the estimate is the standard deviation of the observed xx -values about the predicted xx ^ { \prime } values.

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The prediction interval around yy ^ { \prime } for a specific xx is

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