A. A processing line can combine unites of inputs(X) to produce units of output(Y) such that there • is a linear relationship between X and Y. Given the values of X and Y as follow: 7 5 2 Y 8 14 12 (1) Formulate a simple linear regression equation. (Hi) Determine the value of the correlation coefficient and interpret your result. (ii) Find the value of the coefficient of determination and interpret your results. (iv) What will be the output level if the input is 20? (v) What proportion of the variation in output is not due to X? (vi) Using a = 0.01 test whether the correlation between X and Y are positively linearly correlated. 6.

A. A processing line can combine unites of inputs(X) to produce units of output(Y) such that there • is a linear relationship between X and Y. Given the values of X and Y as follow: 7 5 2 Y 8 14 12 (1) Formulate a simple linear regression equation. (Hi) Determine the value of the correlation coefficient and interpret your result. (ii) Find the value of the coefficient of determination and interpret your results. (iv) What will be the output level if the input is 20? (v) What proportion of the variation in output is not due to X? (vi) Using a = 0.01 test whether the correlation between X and Y are positively linearly correlated. 6.

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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The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.
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?
In an analysis of a sample of bivariate data concerning the soil acidity x (in pH) and germination time y (in days) for tomato seeds, a linear regression model is constructed and follows the equation y^=−1.22x+5y^=−1.22x+5 Select the most appropriate statement about the linear correlation exhibited. A. The data set exhibits strong positive linear correlation. B.We cannot determine anything about the strength or direction of linear correlation from this information alone. C. The data set exhibits strong negative linear correlation. D. The linear correlation coefficient is -1.22.
(b)A random sample of twelve students were chosen, and their midterm test score (  y), assignment score (x1), and missed classes (x2) were recorded as follows: Midterm Score, y Assignment Score, x1 Classes Missed, x2 85 65 1 + Ω 74 50 7 76 55 5 90 65 2 85 55 6 87 70 3 94 65 2 98 70 5 81 55 4 91 70 3 76 50 1 74 55 4 (i)What is the fitted multiple linear regression equation of the form ˆy = b0 + b1x1 + b2x2? (ii)From part 6(b)(i) above, estimate the midterm test score grade for a student who has an assignment score of 60 and missed 4 classes. (iii)Assume that the data on ( y, x1, x2) above in 6(b) is inputted into SPSS, with the following results: ANOVA Source SS df MS F…
(b)A random sample of twelve students were chosen, and their midterm test score (  y), assignment score (x1), and missed classes (x2) were recorded as follows: Midterm Score, y Assignment Score, x1 Classes Missed, x2 85 65 1 + Ω 74 50 7 76 55 5 90 65 2 85 55 6 87 70 3 94 65 2 98 70 5 81 55 4 91 70 3 76 50 1 74 55 4 (i)What is the fitted multiple linear regression equation of the form ˆy = b0 + b1x1 + b2x2? (ii)From part 6(b)(i) above, estimate the midterm test score grade for a student who has an assignment score of 60 and missed 4 classes. (iii)Assume that the data on ( y, x1, x2) above in 6(b) is inputted into SPSS, with the following results: ANOVA Source SS df MS F…
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6.In simple linear regression, the sample correlation coefficient between the input variable and the output variable, and the estimated slope parameter : a.Must have the same sign (negative, zero, or positive) b.May have opposite signs c.Must have opposite signs d.Neither of the above
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