Hours spent studying, x 1 1 3 3 4 6 Test score, y 38 44 50 47 64 70 Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below. (a) x = 2 hours (b) x = 4.5 hours (c) x = 12 hours (d) 1.5 hours Find the regression equation. Construct a scatter plot of the data and draw the regression line. (a) Now use the regression equation to predict the value of y for each of the given x-values, if meaningful. Because the correlation between x and y is significant, the equation of the regression line can be used to predict y-values. However, prediction values are meaningful only for x-values in the range of the data. Begin with x = 2. Since x = 2 is in the range of the original data it is meaningful to predict the value of y for x = 2. Now substitute 2 for x into the regression equation, then calculate ŷ, the predicted y-value. (b) Now predict the value of y for x = 4.5. Since x = 4.5 is in the range of the original data it is meaningful to predict the value of y for x = 4.5. (c) Next predict the value of y for x = 12. Since x = 12 is not in the range of the original data it is not meaningful to predict the value of y for x = 12. (d) Finally predict the value of y for x = 1.5. Since x = 1.5 is in the range of the original data it is meaningful to predict the value of y for x = 1.5

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.CR: Chapter Review Exercises

Problem 15CR: Life Expectancy The following table shows the average life expectancy, in years, of a child born in...

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Hours spent studying, x	1	1	3	3	4	6
Test score, y	38	44	50	47	64	70

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.

(a) x = 2 hours (b) x = 4.5 hours (c) x = 12 hours (d) 1.5 hours

Find the regression equation.

Construct a scatter plot of the data and draw the regression line.

(a) Now use the regression equation to predict the value of y for each of the given x-values, if meaningful. Because the correlation between x and y is significant, the equation of the regression line can be used to predict y-values. However, prediction values are meaningful only for x-values in the range of the data.

Begin with x = 2. Since x = 2 is in the range of the original data it is meaningful to predict the value of y for x = 2.

Now substitute 2 for x into the regression equation, then calculate ŷ, the predicted y-value.

(b) Now predict the value of y for x = 4.5. Since x = 4.5 is in the range of the original data it is meaningful to predict the value of y for x = 4.5.

(c) Next predict the value of y for x = 12. Since x = 12 is not in the range of the original data it is not meaningful to predict the value of y for x = 12.

(d) Finally predict the value of y for x = 1.5. Since x = 1.5 is in the range of the original data it is meaningful to predict the value of y for x = 1.5

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