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Regression Analysis Exercises: Understanding Key Concepts and Applications, Assignments of Mathematics

A series of exercises designed to reinforce understanding of key concepts in regression analysis. It covers topics such as assumptions of the regression model, interpretation of coefficients, calculation of residuals, and the relationship between correlation and determination. The exercises provide practical applications of regression analysis in various fields, helping students develop a deeper understanding of the subject.

Typology: Assignments

2023/2024

Available from 12/18/2024

Milestonee
Milestonee 🇺🇸

4.3

(23)

3.5K documents

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WEEK 6 HOMEWORK
1.
Which of the following is not an assumption of the
regression model?
The error terms have constant
variance
The model is linear
The error terms are normally
distributed
The error terms are
independent
The error terms decrease as x values increase
2.
Suppose for a given data set the regression equation is: y
=
54.78
+
1.45x, and the point (0.00, 24.78) is in the data
set. The residual for this point is .
24.78
−24.78
0.00
30.00
−30.00
3.
If the standard error of the estimate for a regression model
fitted to a large number of paired observations is 1.75,
approximately 68% of the residuals would lie within .
−3.50 and +3.50
−0.95 and +0.95
−0.97 and +0.97
−0.68 and +0.68
−1.75 and +1.75
4.
For a regression model y
=
30
2x, the coefficient of
determination
was determined as equal to 0.81. The coefficient
of correlation is
.
−0.9
pf3
pf4
pf5

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WEEK 6 HOMEWORK

  1. Which of the following is not an assumption of the regression model? The error terms have constant variance The model is linear The error terms are normally distributed The error terms are independent The error terms decrease as x values increase
  2. Suppose for a given data set the regression equation is: y = 54.78 + 1.45 x , and the point (0.00, 24.78) is in the data set. The residual for this point is.
    −24.
    −30.
  3. If the standard error of the estimate for a regression model fitted to a large number of paired observations is 1.75, approximately 68% of the residuals would lie within. −3.50 and +3. −0.95 and +0. −0.97 and +0. −0.68 and +0. −1.75 and +1.
  4. For a regression model y = 30 − 2 x , the coefficient of determination was determined as equal to 0.81. The coefficient of correlation is . −0.
  1. A manager wishes to predict the annual cost ( y ) of an automobile based on the number of miles ( x ) driven. The following model was

developed: y = 2,000 + 0.42 x. If a car is driven 15,000 miles, the predicted cost is. 6, 8, 17, 8, 2,

  1. A manager wishes to predict the annual cost ( y ) of an automobile based on the number of miles ( x ) driven. The following model was developed: y = 2,000 + 0.42 x. If a car is driven 20,000 miles, the predicted cost is. 2, 6, 6, 10, 20,
  2. A hospital administrator developed a regression line, y = 30 + 2 x, to predict y = the number of full-time employees (FTE) needed using x = the number of beds. The slope of this regression line suggests this:. for a unit increase in the number of beds, the number of FTEs is predicted to increase by 2 for a unit increase in the number of beds, the number of FTEs is predicted to decrease by 32 for a unit increase in the number of beds, the number of FTEs is predicted to decrease by 32 for a unit increase in the number of beds, the number of FTEs is predicted to increase by 32

production run

  1. Given a set of paired data, { X , Y }, if Y is independent of X , you would expect that the correlation coefficient is. negative zero positive any value between −1.0 and 1. any value between −0.5 and 0.
  2. Determine the Pearson product-moment correlation coefficient for the following data. x 1 10 9 6 5 3 2 y 9 4 5 5 7 7 8 Correlation coefficient, r = -0.
  3. A numerical measure that indicates the strength of relationship between matched observations of two variables is. the median the correlation coefficient the mean the standard deviation