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MATH225 Week 8 Final Exam
Question
The table shows data collected on the relationship between the time spent studying per day and
the time spent reading per day. The line of best fit for the data is y ˆ=0.16 x +36.2. Assume the
line of best fit is significant and there is a strong linear relationship between the variables.
Studying (Minutes) 507090110 Reading (Minutes) 44485054
(a) According to the line of best fit, what would be the predicted number of minutes spent
reading for someone who spent 67 minutes studying? Round your answer to two decimal places.
Perfect. Your hard work is paying off 😀
The predicted number of minutes spent reading is 46 point 9 2$$46.9246 point 9 2 - correct.
response - correct
Answer Explanation
The predicted number of minutes spent reading is 1 $$1 - no response given.
Correct answers:
(^1) 46 point 9 2 $46.92$46.
Substitute 67 for x into the line of best fit to estimate the number of minutes spent reading for
someone who spent 67 minutes studying: y ˆ=0.16(67)+36.2=46.92.
Question
The table shows data collected on the relationship between the time spent studying per day and
the time spent reading per day. The line of best fit for the data is y ˆ=0.16 x +36..
Studying (Minutes) 507090110 Reading (Minutes) 44485054
(a) According to the line of best fit, the predicted number of minutes spent reading for someone
who spent 67 minutes studying is 46..
(b) Is it reasonable to use this line of best fit to make the above prediction? Great work! That's correct. The estimate, a predicted time of 46.92 minutes, is both reliable and reasonable. The estimate, a predicted time of 46.92 minutes, is both unreliable and unreasonable. The estimate, a predicted time of 46.92 minutes, is reliable but unreasonable. The estimate, a predicted time of 46.92 minutes, is unreliable but reasonable.
Answer Explanation
Correct answer:
The estimate, a predicted time of 46.92 minutes, is both reliable and reasonable.
The data in the table only includes studying times between 50 and 110 minutes, so the line of
best fit gives reliable and reasonable predictions for values of x between 50 and 110. Since 67
is between these values, the estimate is both reliable and reasonable.
Question
Michelle is studying the relationship between the hours worked (per week) and time spent reading (per day) and has collected the data shown in the table. The line of best fit for the data is
y ˆ=−0.79 x +98.8. Assume the line of best fit is significant and there is a strong linear
relationship between the variables.
Hours Worked (per week) 30405060 Minutes Reading (per
day) 75685852
(a) According to the line of best fit, what would be the predicted number of minutes spent
reading for a person who works 27 hours (per week)? Round your answer to two decimal places,
as needed.
The estimate, a predicted time of 77.47 minutes, is reliable but unreasonable. The estimate, a predicted time of 77.47 minutes, is both unreliable and unreasonable. The estimate, a predicted time of 77.47 minutes, is both reliable and reasonable.
Answer Explanation
Correct answer:
The estimate, a predicted time of 77.47 minutes, is unreliable but reasonable.
The data in the table only includes the time worked between 30 and 60 hours, so the line of best
fit gives reliable and reasonable predictions for values of x between 30 and 60. Since 27 is not
between these values, the estimate is not reliable. However, 77.47 minutes is a reasonable time.
Question
A medical experiment on tumor growth gives the following data table. x y
The least squares regression line was found. Using technology, it was determined that the total
sum of squares (SST ) was 3922.8 and the sum of squares of regression (SSR ) was
3789.0. Calculate R 2 , rounded to three decimal places.
Great work! That's correct. 0 point 9 6 6$$0.9660 point 9 6 6 - correct
Correct answers:
Answer Explanation
$$no response given Correct answers: 00 point 9 6 6$0.966$0.
R 2 = SSRSST
R 2 =3789.03922.
R 2 =0.
Something's not right... There is an error in the instruction or question. This looks broken... A graph/image/equation/video isn't working I cannot enter my answer. A problem is preventing me from entering an answer to this question. I have an idea! I have some feedback/suggestions.
Question
A scientific study on mesothelioma caused by asbestos gives the following data table. Micrograms of asbestos inhaled Area of scar tissue (cm^2 )
R 2 =1−903.511421.
R 2 =1−0.
R 2 =0.
R 2 =36.43%
Question
A new mine opened and the number of dump truck loads of material removed was recorded. The table below shows the number of dump truck loads of material removed and the number of days since the mine opened. Days (since opening) # of dump truck loads
A least squares regression line was found. Using technology, it was determined that the total sum
of squares (SST ) was 278.0 and the sum of squares of regression (SSR ) was 274.3. Use
these values to calculate the coefficient of determination. Round your answer to three decimal places. That's incorrect - mistakes are part of learning. Keep trying!
Answer Explanation
Correct answer:
R 2 = SSRSST
R 2 =274.3278.
R 2 =0.
Your answer:
The coefficient of determination is SSRSST and not the square root of that value. Something's not right... There is an error in the instruction or question. This looks broken... A graph/image/equation/video isn't working I cannot enter my answer. A problem is preventing me from entering an answer to this question. I have an idea! I have some feedback/suggestions.
Question
A new mine opened and the number of dump truck loads of material removed was recorded. The table below shows the number of dump truck loads of material removed and the number of days since the mine opened. Days (since opening) # of dump truck loads
x y
A least squares regression line was found. Using technology, it was determined that the total sum
of squares (SST ) was 46.8 and the sum of squares of regression (SSR ) was 14.55. Use
these values to calculate the percent of the variability in y that can be explained by variability in
the regression model. Round your answer to the nearest integer. That's incorrect - mistakes are part of learning. Keep trying! 31% 69% 0.69% 13%
Answer Explanation
Correct answer:
R 2 = SSRSST
R 2 =14.5546.
R 2 =0.
R 2 =31%
Your answer:
The coefficient of determination is SSRSST and not 1− SSRSST.
Something's not right... There is an error in the instruction or question. This looks broken... A graph/image/equation/video isn't working I cannot enter my answer. A problem is preventing me from entering an answer to this question. I have an idea! I have some feedback/suggestions.
Question
A fishing enthusiast puts out different numbers of lines at once on several fishing trips to the same location and records the number of fish he catches on each trip. The table below shows the number of lines and number of fish caught on his trips. Fishing lines Fish caught 4 13 5 15 7 25 11 29 12 26
Using technology, it was determined that the total sum of squares (SST) was 203.20 and the
sum of squares of error (SSE) was 41.62. Use these values to calculate the coefficient of
determination.
Calorie intake (1000) Weight gained (Ounces)
Using technology, it was determined that the total sum of squares ( SST ) was 237.2 , the sum
of squares regression ( SSR ) was 177.96 , and the sum of squares due to error ( SSE ) was
59.244. Calculate R 2 and determine its meaning. Round your answer to four decimal places.
Not quite right - check out the answer explanation. R 2 =0. Therefore, 24.98% of the variation in the observed y -values can be explained by the estimated regression equation. R 2 =0. Therefore, 75.03% of the variation in the observed y -values can be explained by the estimated regression equation. R 2 =1. Therefore, 13.329% of the variation in the observed y -values can be explained by the estimated regression equation. R 2 =0. Therefore, 33.29% of the variation in the observed y -values can be explained by the estimated regression equation.
Answer Explanation
Correct answer:
R 2 =0.
Therefore, 75.03% of the variation in the observed y -values can be explained by the estimated
regression equation.
R 2 = SSRSST
R 2 =177.96237.
R 2 =0.
R 2 =75.03%
Your answer:
R 2 =0.
Therefore, 24.98% of the variation in the observed y -values can be explained by the estimated
regression equation. The coefficient of determination is SSRSST and not SSESST
Question
A scientific study on graphite density gives the following data table. Distance from center of vein Density
Using technology, it was determined that the total sum of squares ( SST ) was 542.07 , the sum
of squares regression ( SSR ) was 521.02 , and the sum of squares due to error ( SSE ) was
21.044. Calculate R 2 and determine its meaning. Round your answer to four decimal places.
Perfect. Your hard work is paying off 😀 R 2 =0. Therefore, 3.88% of the variation in the observed y -values can be explained by the estimated regression equation. R 2 =0.
Given the SSE , SSR , and SST , find the variance in the dependent variable that can't be
explained by the variance in the independent variable.
SSE 15
SSR 25
SST 40
Answer 1: Keep trying - mistakes can help us grow.
5 $$55 - incorrect
Answer 2: Not quite - review the answer explanation to help get the next one.
5 $$55 - incorrect
Answer Explanation
Correct answers:
The sum of squares due to error, SSE , is 15 , which is equal to the variance in the dependent
variable, y , that can't be explained by the variance in the independent variable, x.
Given the SSR and SSE , find SST.
SSR 48
SSE 28
Answer 1: That's not right - let's review the answer.
100 $$100100 - incorrect
Answer 2: Keep trying - mistakes can help us grow.
10 $$1010 - incorrect
Answer Explanation
Correct answers:
SST = SSR + SSE
SST =48+
SST =
Question
For a particular regression equation, SSR =325 and SST =550. What is SSE?
Answer 1: That's incorrect - mistakes are part of learning. Keep trying!
875 $$875875 - incorrect
Answer 2: Well done! You got it right.
225 $$225225 - correct
Answer Explanation
Correct answers:
Substitute the given values for SST and SSR into the relationship SST = SSR + SSE and solve
for SSE.
SST 550550−325 SSE = SSR + SSE =325+ SSE = SSE =
Question
A scientific study on construction delays gives the following data table. Construction delay (hours) Increased cost ($1000)
Using technology, it was determined that the total sum of squares ( SST ) was 2542.8 , the sum
of squares regression ( SSR ) was 2194.8 , and the sum of squares due to error ( SSE ) was
347.99. Calculate R 2 and determine its meaning. Round your answer to four decimal places.
Great work! That's correct. R 2 =0. Therefore, 86.31% of the variation in the observed y -values can be explained by the estimated regression equation. R 2 =1. Therefore, 1.1586% of the variation in the observed y -values can be explained by the estimated regression equation. R 2 =0. Therefore, 13.69% of the variation in the observed y -values can be explained by the estimated regression equation. R 2 =0. Therefore, 15.86% of the variation in the observed y -values can be explained by the estimated regression equation.
Answer Explanation
Correct answer:
R 2 =0.
Therefore, 86.31% of the variation in the observed y -values can be explained by the estimated
regression equation.
R 2 = SSRSST
R 2 =2194.82542.
R 2 =0.
R 2 =86.31%
Question
Given the SSE , SSR , and SST , find the variance in the dependent variable that can be
explained by the variance in the independent variable.
SSE 2
SSR 6
SST 8
Correct! You nailed it.
6 $$66 - correct
Answer Explanation
Correct answers:
The sum of squares of regression, SSR , is 6 , which is equal to the variance in the dependent
variable, y , that can be explained by the variance in the independent variable, x.
Question
