How do you find the coefficient of determination?
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Exercises
Use the data to find the coefficient of determination and the standard error of estimate.
x 1 2 3 4 5 6
y 12 7 10 3 6 4
The equation of the regression line is y = 12 - 1.42857x.
Find the coefficient of determination.
y^2 = _______. (Round to the nearest thousandth.)
The table shows median weekly earnings (in U.S. dollars) of full-time male and female workers for five years. The equation of the regression line is y = 0.508373x + 174.8.
Median weekly earnings of male workers, x 679 672 618 557 639
Median weekly earnings of female workers, y 552 529 511 473 418
Find the coefficient of determination.
y^2 = ______. (Round to the nearest thousandth.)
Construct a 95% prediction interval for the y-value when the value fo x = 2.5.
x 1 2 3 4 5 6
y 11 7 9 4 6 3
The prediction equation is y = 11.4667 - 1.37143x. The standard error of estimate is 1.7619.
Find a 95% prediction interval for the y-value when x = 2.5. Do not round until the final answer.
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Solution Summary
The solution does a great job of explaining the problem below. Step by step instructions are provided to arrive to the final answer. The solution can be easily understood by a student with a basic understanding of Statistics. The attachment solves the solution in Excel as well. A word document has also been provided to assist the student. Overall, a great response.
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
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