15.23. You are given the following observations on X and Y136.8.1254Using linear regression of Y on X, estimate the proporation of varianceof Y due to X. Also give the proportion of variance of Y which remainsunexplained.

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Answered: 15.23. You are given the following…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 2AGP

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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?
What percentage of the variation in can be explained by the corresponding variations in and taken together?
Suppose we perform a simple linear regression (SLR) of two variables F1 and F2 against the same out variable (say y). The r-squared value/score of both the SLRS are 0.9678 and 0.95123 respectively for F1 and F2. Then what can you say about the correlation? O a. y is more dependent on F2 than F1 O b. None of these O . The result does not say that y is more dependent on F1 OR F2 O d.y is more dependent on F1 than F2
The fish in my pond have mean lenth 14 inches with a standard deviation of 2 inches and mean weight 4 pounds with a standard deviation of .8 pounds. The correlation coefficient of length and weight is .4. If the length of a particular randomly selected fish is reported to be 15 inches, then what should we predict for the weight of that fish using simple linear regression?
1) Match each of the five scatterplots to the appropriate correlation coefficient and equation of regression line. Explain how you know that you have made a correct match. a. r= 0.83, y= -2.1 + 1.4x d. r= -0.83, y = 11.8 – 1.4x b. r= -0.31, y = 7.8 – 0.5x e. r= 0.41, y=1.4 + 1.4x c. r= 0.96, y= -2.1 + 1.4x Scatterplot 1 Scatterplot 2 Scatterplot 3 Scatterplot 4 Scatterplot 5
There exists a moderate relationship between the variables x and y.if we draw samples of increasing sample size,what can we expect from the sample r value,the regression slope and the p value of the regression or correlation be affected by increasing sample size
A professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n = 15 college students. The SAT scores have a mean of M = 580 with SS = 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84. Find the regression equation for predicting GPA from SAT scores. What percentage of the variance in GPAs is accounted for by the regression equation? (Compute the correlation r, then find r^2.) Does the regression equation account for a significant portion of the variance in GPA? Use α = .05 to evaluate the F-ratio.
In linear regression, the mean value of all residuals will be greater for a correlation of -.70 than for a correlation of O -60 O.89 O -2 O.34
After performing a statistical regression on a set of data the value of the correlation coefficient r was -0.2041. What does that imply about the data?
In a partially destroyed laboratory, record of an analysis of correlation, data, the following results only are legible:Variance of X=9. Regression equation: 8X –10Y + 66=0, 40X–18Y = 214.(1) the mean value X and Y,(2) the correlation coefficient between X and Y, and (3) the standard deviation of Y ?
A professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n=15 college students. The SAT scores have a mean of M=580 with SS = 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84. Find the regression equation for predicting GPA from SAT scores. What percentage of the variance in GPAs is accounted for by the regression equation? (Compute the correlation, r, then find r2.) C) Does the regression equation account for a significant portion of the variance in GPA? Use alpha = 0.05 to evaluate the F-ratio. A) b=0.00375; a=0.925; Y (hat) = 0.00375X+0.925 B) r= 0.5 r^2= 0.25
4. A runner was tested on a treadmill. During the test, his speed x (in km/h) and his heart rate y were measured. The results are shown in the table. y 122 132 145 161 178 190 x 8 10 12 14 16 18 (a) Test for the significance of regression using the analysis of variance with a = 0.05. Find the P-value for this test. Can you conclude that the model specifies a useful linear relationship between these two variables? (b) Estimate ². (c) Estimate the standard error of the slope and intercept in this model. (d) Test the hypothesis that the increase in the speed of 1 km/h results in the runner's heart rate average increase of 7 points at a = 0.05. Suppose that the alternative hypothesis is that the average increase of the runner's heart rate in this situation does not equal 7 points.

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15.23. You are given the following observations on X and Y 1 3 8 Y 1 3 2 5 4 Using linear regression of Y on X, estimate the proporation of variance of Y due to X. Also give the proportion of variance of Y which remains unexplained. -