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Regression Analysis: Homework and Quiz Review, Quizzes of Mathematics

A comprehensive review of key concepts and exercises related to regression analysis. It covers topics such as regression equations, slope, y-intercept, correlation coefficient, coefficient of determination, residuals, and hypothesis testing. Worked-out examples and explanations, making it a valuable resource for students studying regression analysis.

Typology: Quizzes

2023/2024

Available from 12/18/2024

Milestonee
Milestonee 🇺🇸

4.4

(22)

3.5K documents

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Week 6 ADDENDUM Homework/Quiz Review
These are some additional notes that might help with the homework and quiz.
1. You can skip #16 in the homework and #9 and #10 in the quiz. Everyone will be given credit.
The problems look something like this:
In the regression equa
ti
on, ŷ = 5.23 + 2.74x, and n = 24, the mean of x is 12.56, SS
xx
=
55.87 and S
e
= 10.71. A 90% predic
ti
on interval for y when x = 11 is .
2. Review definitions and concepts in the notes.
3. We are developing a regression model to predict weight as function of height.
a. What is the explanatory variable (independent variable)? Answer: height
b. What is the response variable (dependent variable)? Answer: weight
4. In the following regression: ŷ = 27.7 + 3.25x
a. What is the slope? Answer: 3.25
b. What is the y-intercept? Answer: 27.7
5. Use the following data to construct a regression model:
X 27 34 23 17 18
Y 5 14 8 2 5
Answer: ŷ = -6.61 + 0.56x
Independent (x) Dependen t
(y)
Slope (β1) y-Intercept (β0)
Correlation Coefficient (r)
Coefficient of Determination (r2)
Standard Error
27 5
34 14
23 8
17 2
18 5
0.563655
-6.614990
0.864555
0.747456
2.640119
pf3
pf4
pf5

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Week 6 ADDENDUM – Homework/Quiz Review These are some additional notes that might help with the homework and quiz.

  1. You can skip #16 in the homework and #9 and #10 in the quiz. Everyone will be given credit. The problems look something like this: In the regression equation, ŷ = 5. 2 3 + 2 .7 4 x, and n = 24, the mean of x is 1 2. 5 6, SSxx = 55. 87 and Se = 1 0.7 1. A 9 0% prediction interval for y when x = 11 is.
  2. Review definitions and concepts in the notes.
  3. We are developing a regression model to predict weight as function of height. a. What is the explanatory variable (independent variable)? Answer: height b. What is the response variable (dependent variable)? Answer: weight
  4. In the following regression: ŷ = 27.7 + 3.25x a. What is the slope? Answer: 3. b. What is the y-intercept? Answer: 27.
  5. Use the following data to construct a regression model: X 27 34 23 17 18 Y 5 14 8 2 5 Answer: ŷ = -6.61 + 0.56x Independent (x) (^) Dependen t (y) Slope (β 1 ) y-Intercept (β 0 ) Correlation Coefficient (r) Coefficient of Determination (r^2 ) Standard Error

-6.

16 14 12 10 8 6 4 2 0 0 R² =2 0 .08 406080100120140

  1. For the following scatter plot and regressionline, at x=26, is the residual negative, positive or zero? f(x) = - 0.01 x + 1.0 7 Answer: Negative Explanation: - residual = y – ŷ - For x=26, ŷ is bigger than y (e.g. approximately 8 vs approx 5) - Therefore y- ŷ will be negative
  2. If the coefficient of determination (r-squared) is .81, what is the correlation coefficient (r)? Answer: -0.9 or 0. Explanation: - The coefficient of correlation (R) is square root of coefficient of determination (R- squared). - So if R-squared is .81, it’s square root could be 0.9 or -0.
  3. If the coefficient of correlation is -0.9, what is the coefficient of determination? Answer: 0. Explanation: - Same logic as the problem above, except we are convert r to r-squared.
  4. We want to predict weight (y) based on height (x). The following equation shows the relationship: ŷ = 70 + 1.3x. If someone is 65 inches tall, what would the predicted weight be? Answer: 154. Explanation: - Plug in 65 for x in the equation.a trip took - ŷ = 70 + 1.3x = 70 + 1.3*65 = 154.
  5. In the equation ŷ = 70 + 1.3x, what is the x- intercept? Answer: -53. Explanation:
    • Problem is asking for x-intercept, NOT y-intercept
    • x-intercept is the value of x when y=
    • You can plug in 0 for ŷ and solve for x. OR you can just use the following formula: x-intercept = ( -1 * y-intercept ) / slope = (-1 * 70) / 1.3 = -53.

a. What type of correlation exists for this data? Answer: Strong negative correlation Explanation: The coefficient of correlation is -0.84. This is considered a strong negative correlation. The scatter plot confirms this. The following output is from this week’s calculator. b. What is the 90% confidence interval for children who are 12 years old? Answer: (18.92, 21.72) c. What is the 90% prediciton interval for someone who is 12 years old. Answer: (16.16, 24.48) Independent (x) (^) Dependent (y) Slope (β 1 ) y-Intercept (β 0 ) Correlation Coefficient (r) Coefficient of Determination (r^2 ) Standard Error

Confidence Interval For Slope

Lower Limit -3. Upper Limit -1. Enter x-value 12 CONFIDENCE LEVEL FOR ALL INTERVALS 90% Mean (x) 12. y estimate for entered x value 20. SSx 8. Standard Error Confidence Interval 0. Standard Error Prediction Interval 2.

Confidence Interval for Given x

Lower Limit Upper Limit

Prediction Interval for Given x

Lower Limit Upper Limit

-2.

-0.

1 0.9 f(x)^ =^ −^ 0.06^ x^ +^ 4.91^ R²^ = 0.

0 9 29496989109129149

  1. True/False. A plot of the residuals should show a constant variance. Answer: True Explanation: When you plot the residuals, they must have uniform (constant) variance as shown in the third graph below. They should not have a nonconstant variance, as shown in the in the first two graphs below.