Interpreting Simple Linear Regression 1. Linear correlation coefficient r = 0.794556 2. Coefficient of Determination ( r square) 0.631319 3. Standard Error of the estimate = 12.9668 4. SSR (Explained variation) = 5182.41 5. SSE ( Unexplained variation) = 3026.49 6. SST = 8208.90 7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523 8. Level of Significance = 0.1 9. Critical Value= 0.378419 10. t test = 0.794556 Question What is meant by a hypothesis? State the hypothesis in this example? A hypothesis is a claim about the correlation between the Y and X variables in the population

Interpreting Simple Linear Regression 1. Linear correlation coefficient r = 0.794556 2. Coefficient of Determination ( r square) 0.631319 3. Standard Error of the estimate = 12.9668 4. SSR (Explained variation) = 5182.41 5. SSE ( Unexplained variation) = 3026.49 6. SST = 8208.90 7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523 8. Level of Significance = 0.1 9. Critical Value= 0.378419 10. t test = 0.794556 Question What is meant by a hypothesis? State the hypothesis in this example? A hypothesis is a claim about the correlation between the Y and X variables in the population

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
a. Determine the correlation coefficient r between the two variables. b. Determine the slope coefficient β1 for the regression of marks on study time. c. What will be the expected marks of a student who studied for 33 hours?
The standardized regression coefficient describes the relationship between X and Y in terms of ______. Group of answer choices the correlation between observed and predicted scores standard deviations the original units of measurement partitions of variance
randomly selected middle school students. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 1.5 2 3 3.5 4 4.5 5.5 Overall Grades 99 96 84 75 68 65 60 Table Step 1 of 6 : Find the estimated slope. Round your answer to three decimal places.
randomly selected middle school students. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 1.5 2 3 3.5 4 4.5 5.5 Overall Grades 99 96 84 75 68 65 60 Table Find the estimated slope, y interscept and correlation coefficient Round your answers to three decimal places.
With the help of the observations of X and Y variables;a) Estimate and graph the regression equation.b) Estimate the Y value for X = 9.c) Calculate the correlation coefficient. Determine the direction and degree of this relationshipd) Test the hypothesis that p is not different from zero for α = 0.01 and α = 0.05 significance level.
Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?
Find the slope of regression line, y-intercept of regression line, coefficient of determination (r^2), and the linear correlation coefficient (r)
Find the simple regression line y=α+βx for the pairs of points belonging to the independent and dependent variables (xi,yi) , respectively. Also, interpret the result by calculating the Pearson correlation coefficient. Please dont use excel. Use paper.dont use computer
The coefficient of determination of a set of data points is 0.716. a. Can you determine the linear correlation coefficient? If yes, obtain it. If no, why not? b. Can you determine whether the slope of the regression line is positive or negative? Why or why not? c. If we tell you that the slope of the regression line is negative, can you determine the linear correlation coefficient? If yes, obtain it. If no, why not? d. If we tell you that the slope of the regression line is positive, can you determine the linear correlation coefficient? If yes, obtain it. If no, why not?
A linear relationship exists between two variables x and y. The correlation coefficient was calculated for the sample data and is equal to -0.93. Using the estimated regression equation, a straight line that will best fit the data points can be drawn through the points on the scattergram.The line slopes downward from left to right and the points are scattered close to the line. True or false
The final test and exam averages for 20 randomly selected students taking a course in engineering statistics and a course in operations research follow. Assume that the final averages are jointly normally distributed.Find the regression line relating the statistics final average to the OR final average.(c) Estimate the correlation coefficient.