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(1) Let x be the age in years of a licensed automobile driver. Let y be the percentage of all fatal accidents (for a given age) due to speeding. For example, the first data pair indicates that 33% of all fatal accidents of 17-year-olds are due to speeding.

 x 17 27 37 47 57 67 77 y 33 28 22 12 10 7 5

Complete parts (a) through (e), given

Σx = 329, Σy = 117, Σx2 = 18,263, Σy2 = 2675, Σxy = 4119, and r ≈ −0.972.

(a) Draw a scatter diagram displaying the data.

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(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)
 Σx = Σy = Σx2 = Σy2 = Σxy = r =

(c) Find x, and y. Then find the equation of the least-squares line  = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)
 x = y = = +  x

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)
 r2 = explained % unexplained %

(f) Predict the percentage of all fatal accidents due to speeding for 35-year-olds. (Round your answer to two decimal places.)
%

(2) Let x be the age of a licensed driver in years. Let y be the percentage of all fatal accidents (for a given age) due to failure to yield the right of way. For example, the first data pair states that 5% of all fatal accidents of 37-year-olds are due to failure to yield the right of way.
 x 37 47 57 67 77 87 y 5 8 10 15 27 44
Complete parts (a) through (e), given Σx = 372, Σy = 109, Σx2 = 24814, Σy2 = 3079, Σxy = 8043, and r ≈ 0.927.
(a) Draw a scatter diagram displaying the data.

Flash Player version 10 or higher is required for this question.
You can get Flash Player free from Adobe's website.

(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)
 Σx = Σy = Σx2 = Σy2 = Σxy = r =

(c) Find x, and y. Then find the equation of the least-squares line  = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)
 x = y = = +  x

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.
(e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)
 r2 = explained % unexplained %

(f) Predict the percentage of all fatal accidents due to failing to yield the right of way for 75-year-olds. (Round your answer to two decimal places.)

(3) Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y.
 x 8.2 9.2 10.2 8 8.3 8.7 y 9.9 18.2 21 10.2 11.4 13.1
Complete parts (a) through (e), given Σx = 52.6, Σy = 83.8, Σx2 = 464.5, Σy2 = 1275.86, Σxy = 753.01, and r ≈ 0.974.
(a) Draw a scatter diagram displaying the data.

Flash Player version 10 or higher is required for this question.
You can get Flash Player free from Adobe's website.

(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)
 Σx = Σy = Σx2 = Σy2 = Σxy = r =

(c) Find x, and y. Then find the equation of the least-squares line  = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)
 x = y = = +  x

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)
 r2 = explained % unexplained %

(f) Suppose a small city in Oregon has a per capita income of 9.3 thousand dollars. What is the predicted number of M.D.s per 10,000 residents? (Round your answer to two decimal places.)
M.D.s per 10,000 residents

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Step 1

Hello. Since you have posted multiple questions and not specified which question needs to be solved, we will solve the first three sub-parts of the first question for you. If you want any other specific question to be solved then please resubmit only that question or specify the question number.

(a)

The scatter diagram for the provided data can be plotted using Excel.

The steps are given below:

1. Enter the data into Excel sheet.
2. Select the data and click on ‘Insert’ in the tool bar.
3. In the charts, select the scatter plot.
4. Click on ‘Design’ in the toolbar and ‘Add chart element’. Name the axis titles and chart title.

The scatterplot is shown below: help_outlineImage TranscriptioncloseScatterplot 35 X 30 17 33 27 28 25 37 22 20 47 12 15 10 57 10 67 7 77 10 20 30 40 50 60 70 80 90 X From the above plot, it can be observed that there is a strong negative correlation between x and y O un fullscreen
Step 2

(b)

The calculations are... help_outlineImage Transcriptioncloseχν Χ 17 33 289 1089 561 27 28 729 784 756 37 22 1369 484 814 2209 47 12 144 564 57 10 3249 100 570 7 469 67 4489 49 77 5 5929 25 385 Σ ΣΥ-1 Σ3263| Σ-2675Σν-411 x 329 Σν-Σ)(Σ) Σ-ΣΣ-Σ )] 7(4119)-(329)(117) 718263)-(5297(2675)-(117] |-0.972 Therefore, Σν17 | Σ-18263 | Σ-2675| Σw-4119 Σ:329 r-0.972 The values are verified fullscreen

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