Please answer the whole question. (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.x17273747576777y332822121075Complete 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. 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 speeding for 35-year-olds. (Round your answer to two decimal places.) %

Question
Asked Jul 21, 2019
14 views

Please answer the whole question. 

(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.

 
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 speeding for 35-year-olds. (Round your answer to two decimal places.)
 %
check_circle

Expert Answer

Step 1

Hello there! There are more than three sub parts in the given question. According to our policies cannot solve more than three sub parts per session. Kindly find solution for part a, b and c. If you have any doubts in remaining parts of question kindly make a new request.

Given data of x be the age in years of licensed automobile driver and y be percentage of fatal accidents and its scatter plot is shown below.

33
35
28
30
22
15
12
10
10
10
20
30
40
50
60
70
80
90
age of licensed automobile driver (x)
17
33
27
28
37
22
47
12
57
10
67
77
5
7
V
un .
20
O
Fatal accidants percentage
help_outline

Image Transcriptionclose

33 35 28 30 22 15 12 10 10 10 20 30 40 50 60 70 80 90 age of licensed automobile driver (x) 17 33 27 28 37 22 47 12 57 10 67 77 5 7 V un . 20 O Fatal accidants percentage

fullscreen
Step 2

From given data we calculate the required sums to and use the correlation coeffi...

Χ^2
y^2
Χ
Σ
33
xy
561
17
289
1089
1
2
27
28
729
784
756
3
37
22
1369
484
814
47
12
2209
144
564
4
5
57
10
3249
100
570
67
7
4489
49
469
25
7
77
5
5929
385
Total Σx=329 Σy 117 Σ^2132 63| Σy2 2675| Σν 4119|
n (Σ3v)-(Σ x(Σy)
ν ηΣ-Σ) (ΗΣΥ - (Σy)
7(4119)-(329 117)
ν(7*18263- (329)*)(7 * 2675 - (117')
9660
=-0.972
ν19600) (503 6)
help_outline

Image Transcriptionclose

Χ^2 y^2 Χ Σ 33 xy 561 17 289 1089 1 2 27 28 729 784 756 3 37 22 1369 484 814 47 12 2209 144 564 4 5 57 10 3249 100 570 67 7 4489 49 469 25 7 77 5 5929 385 Total Σx=329 Σy 117 Σ^2132 63| Σy2 2675| Σν 4119| n (Σ3v)-(Σ x(Σy) ν ηΣ-Σ) (ΗΣΥ - (Σy) 7(4119)-(329 117) ν(7*18263- (329)*)(7 * 2675 - (117') 9660 =-0.972 ν19600) (503 6)

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Advanced Topics in Statistics

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: Use a χ2​-test to test the claim σ2=0.49 at the α=0.10 significance level using sample statistics s2...

A: In order to test the hypothesis of H0: sigma square  is equal to 0.49  versus Ha: sigma square not e...

question_answer

Q: Simple random sampling uses a sample of size from a population of size to obtain data that can be us...

A: The population size is denoted by ‘N’ and the sample size is denoted by ‘n’.Let the number of differ...

question_answer

Q: A set of data items is normally distributed with a mean of 40 and a standard deviation of 6. Convert...

A: Given set of data is normally distributed with mean = 40Standard deviation = 6The Z score for any da...

question_answer

Q: (c) Compute the sample correlation coefficient r for each of the following data sets and show that r...

A: Sample correlation coefficient:The Karl Pearson’s product-moment correlation coefficient or simply, ...

question_answer

Q: It is thought that prehistoric Indians did not take their best tools, pottery, and household items w...

A: Given data obtained for a collection of archeological sites in New Mexico as shown below. The least ...

question_answer

Q: how do I compute six deviations (x scores are [0,1,1,1,2,7,]) from the mean (x-m), and list these si...

A: Solution:Calculation of mean:The mean of X scores is calculated as follows.

question_answer

Q: 2.) Two distinct fair dice are rolled at the same time and the number of dots appearing on both are ...

A: Probability that the sum is 3It is possible only in following combinations:Dice one has 1 dice and d...

question_answer

Q: 2. The following table represents the carbon emissions in millions of tons from consumption of fossi...

A: (a) Point estimate and standard deviation:Point estimate:The general formula to obtain the mean of a...

question_answer

Q: A political candidate has asked you to conduct a poll to determine what percentage of people support...

A: As there is no any estimates available, the sample proportion is assumed to be 0.50, that is, 50%.He...