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Coordinate Algebra EOC (GSE) Quiz Answer KeyInterpreting Categorical and Quantitative Data - (MGSE9‐12.S.ID.6a ) Fit A Function

Student Name: _______________________ Date: _________Teacher Name: THUYNGA DAO Score: _________

1)

Using the line of best fit, estimate a person's hourly rate when he or she has 5 years of experience.

A) $11

B) $12

C) $13

D) $14

Explanation:The solution is $11. Looking at the graph, we see that the hourly rate increases about $1 with each year of experience. With 4 yearsof experience, the hourly rate is about $10. Therefore, with 5 years of experience, the salary will be about $11.



2)

Which description BEST describes the correlation?

A) no correlation

B) prime correlation

C) positive correlation

D) negative correlation

Explanation:The solution is positive correlation. If we sketch the line of best fit, we can determine that the slope is positive.

3)

The graph shows the stock value for a technology company from 2002 to 2005. From this graph, what is the most likely value of thestock for the year 2006?

A) $40

B) $50

C) $60

D) $70

Explanation:The solution is $70. From 2002-2005 the stock value increases $10 each year. Based on this pattern we see that the most probablevalue for 2006 is $70.



4)

Which of the choices is NOT a good example of a line of best fit?

A)

B)

C)

D)

Explanation:The solution is B. The line in choice B is not a good match for the scatterplot.



5)

The scatterplot compares the price of gasoline (in dollars) and the number of hybrid cars sold in Georgia.

Based on the trend, predict the number of hybrid cars sold if the price of gas is $4.00 a gallon.

A) 8

B) 800

C) 8,000

D) 80,000

Explanation:The correct answer is 8,000. As gas prices increase the number of hybrid cars sold has increased. At $3.45 a gallon 5,800 cars hadbeen sold so at $4.00 a gallon approximately 8,000 could be sold



6)

Which of the graphs is the best example of a line of best fit?

A)

B)

C)

D)

Explanation:The solution is A. The line in choice A is the most closely correlated with the scatterplot.

7)

Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Numberof Birds

2 10 5 16 6 15 20 12 28 30 28 35 37 32 45 39 56 52 60 65

Natalie counted the number of birds she saw each day for 20 days, and she recorded her data in the table. Which scatterplotcorrectly displays Natalie’s data?

A)



B)

C)

D)

Explanation:Scatterplot A correctly shows Natalie's data.



8)

The table contains the data of two variables, X and Y. Which regression line shows the best fit to the random sample observations ofXi and Yi in the table?

A)

B)

C)

D)

Explanation:In this problem we don’t need to know the equation of the regression line. The line best fits the data (predicted values) to be asclose to the actual (observed values) as possible. The differences between the predicted values and the observed values shouldappear as the vertical distances between each observed value and its predicted value. The line that minimizes the sum of the squares of the distances isthe best fit line, or regression line, we are looking for. The correct answer is graph B.

9)



The scatterplot shows the data collected from a survey of 19 students, in which they were asked how many hours per week theystudy (x) and what their GPAs are (y). What relationship, if any, is shown between the two sets of data?

A) There is no correlation between them.

B) There is a positive correlation between them.

C) There is a negative correlation between them.

D) There is an indirect correlation between them.

Explanation:There is a positive correlation between them. Since the points on the graph tend to rise from left to right, the correlation is positive.

10)

From looking only at the scatterplot, a reasonable prediction is that the temperature at 4 pm will be

A) lower than the temperature at 2 pm.



B) lower than the temperature at 3 pm.

C) higher than the temperature at 3 pm.

D) the same as the temperature at 3 pm.

Explanation:higher than the temperature at 3 pm. The temperature is consistently rising every hour. Looking only at the scatterplot and using noother information, it is reasonable to predict that the temperature at 4 pm will be higher than the temperature at 3 pm.

11)

Week (x) 1 2 3 4 5

Number of Customers (y) 30 42 56 72 90

A new business began tracking how many customers entered the store each week. The store owner realized the relationshipbetween the week and the number of customers was quadratic. If the trend continues, during which week will 156 customers enterthe store?

A) week 7

B) week 8

C) week 16

D) week 17

Explanation:Enter the data into a graphing calculator. Then use the "QuadReg" function. On a TI-83, this can be found under the STAT button.

The equation for the data is y = x2 + 9x + 20. Enter 156 for y and solve: x2 + 9x - 136 = 0. Factor (x - 8)(x + 17) = 0. The answercannot be negative so the solution has to be week 8.



12)

linregtable

Hours, x 3 5 2 8 2 4 4 5 6 3

Scores, y 65 80 60 88 66 78 85 90 90 71

The data shown are the final exam scores of 10 randomly selected math students and the number of hours they studied for theexam. The equation of the line of best fit for this data is

A) y = 56.11x - 5.044

B) y = 5.044x + 56.11

C) y = -56.11x - 5.044

D) y = 5.044x + 5.044

Explanation:y = 5.044x + 56.11 is correct. Use a calculator to find the regression line.

13)

The graph shows the relationship between the number of cars horns Sally heard and the amount of time that has passed sincemidnight. She has no data for the 8-hour mark. According to the scatterplot, about how many car horns did she hear at that time?

A) 4

B) 12

C) 18

D) 25

Explanation:Look for 8 on the x-axis and find the y-value that would fit the data. 8 hours after midnight Sally heard about 18 car horns.

14)



Sarah's younger siblings are always bothering her when she does her homework, and she begins to wonder whether other studentshave the same trouble. She surveys 25 of her fellow juniors and records the number of siblings and the homework grades for each ofthem.

According to the scatterplot Sarah produced from this data, which conclusion is MOST justified? [Note: x is the number of siblings, yis the homework grade.]

A) Siblings have a mixed effect on homework performance.

B) Siblings have a positive effect on homework performance.

C) Siblings have a negative effect on homework performance.

D) Siblings have little or no effect on homework performance.

Explanation:Siblings have a negative effect on homework performance. Notice that as x increases y decreases, which indicates a negativecorrelation.



15)

Number of Minutes Studying and Test Grades

Minutes Studying Test Grade

20 65

22 65

25 50

25 52

30 55

30 68

45 70

45 69

60 75

75 80

90 78

90 83

90 85

100 88

100 78

110 95

120 96

120 100

150 91

150 85

160 82

180 80

180 80

Mrs. Blair believes there is a relationship between the number of minutes students study and their test grades. She asked her historyclass to list the number of minutes they studied and their test grade. Using the information provided draw a scatterplot.

What test grade could a student expect if they studied approximately 40 minutes?

A) 65

B) 75

C) 85

D) 95

Explanation:A student could expect to earn about an 65 Looking at a scatterplot go along the x-axis until you get to 40 and then find the y-valueassociated with that.



16)

What type of relationship does there appear to be between the day of the week and the number of newspapers sold?

A) no relationship

B) quadratic relationship

C) exponential relationship

D) positive linear relationship

Explanation:There is no relationship since you cannot find a pattern between the x and y's.

17)

The graph shows Jessica's weight as it compares to her age. Using the line of best fit what is the best approximation for Jessica'sweight at age 9?

A) 70 pounds

B) 75 pounds

C) 80 pounds

D) 85 pounds

Explanation:The solution is 75 pounds. Jessica gains approximately 5 pounds each year. At age 8 she weighs approximately 68 pounds, so if thepattern continues, she will weigh about 75 pounds at age 9.



18)

Jennifer has the scatterplot shown for her data set, where water is measured in ounces, and is trying to describe the line of best fit.

Which choice correctly describes the line of best fit?

A) As the temperature increases, her water intake decreases.

B) As the temperature increases, her water intake increases.

C) As the temperature decreases, her water intake increases.

D) There is no relationship between temperature and water intake.

Explanation:There is a relationship between temperature and water intake Since the line of best fit has a slight positive slope you know thatboth temperature and water intake must be increasing. The correct interpretation is As the temperature increases, her water intakeincreases.



19)

Data from Previous Truck Head Gaskets

Temperature (°C) Damage Index

12 11

13 8

14 8

16 2

18 2

19 2

19 2

19 1

19 1

20 0

21 4

21 0

21 0

Scientists believe there is a link between ambient temperature and damage to a head gasket on a car. Using the providedinformation draw a scatterplot of the data.

If the forecast was for temperatures at 5° Celsius, what recommendation would you give to a truck driver who wanted to leave on atrip? Justify your recommendation.

A) I would recommend that he goes as there were many more temperatures with no damage than with damage.

B)I would recommend that he goes as lower temperatures have a strong positive correlation, therefore the lower thetemperature the less damage is caused.

C)I would recommend that he does not go as lower temperatures have a strong negative correlation, therefore the lower thetemperature the more damage is caused.

D)I would recommend that he does not go as higher temperatures have a strong positive correlation therefore the higherthe temperature the more damage is caused.

Explanation:The correct answer is I would recommend that he does not go as lower temperatures have a strong negative correlation, thereforethe lower the temperature the more damage is caused. For temperatures below 19 degrees Celsius the scatterplot forms a negativecorrelation.

20)



This graph shows the points scored by a basketball team’s star player and the total points scored by the team over a 5 game interval.What can you conclude about the relationship between these two variables?

A) The team scored the most points when the player scored 31 points.

B) As the player’s scoring increases, the team's scoring decreases.

C) As the player’s scoring increases, so does the team’s scoring.

D) There is no obvious relationship between the player’s scoring and the team’s scoring.

Explanation:The graph shows it clearly: as the player’s scoring increases, the team’s scoring decreases.



21)

Rain Fall (x) 13.1 11.4 16.0 15.1 21.4 12.9 9.6 18.2 18.6

Yield (y) 48.5 44.2 56.8 80.4 47.2 29.9 74.0 74.0 76.8

In an area of the Midwest, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels peracre). The data for a 9 year period is given in the table. The equation of the line of best fit for this data is y = 47.3 + 0.78x. How manybushels of wheat per acre can be predicted if it is expected that there will be 17 inches of rain?

A) 5.96

B) 52.06

C) 60.56

D) 65.34

Explanation:60.56 is correct. Plugging in x = 17 yields 60.56 for y.

22)

Judging from this scatter plot, what kind of relationship does there seem to be between the time between eruptions and the lengthof the eruptions?

A) weak linear

B) strong linear

C) weak quadratic

D) strong quadratic

Explanation:There seems to be a strong linear relationship. Linear, because it is one-directional; strong, because the points are closely gatheredtoward a line.

23)



What type of relationship does there appear to be between the number of soft drinks consumed per week and the age of theconsumer?

A) no relationship

B) quadratic relationship

C) exponential relationship

D) positive linear relationship

Explanation:As the age of the consumer increases so does the number of soft drinks. It appears that they increase at a constant rate. Therefore,the relationship is an positive linear relationship



24)

Number of Minutes Studying and Test Grades

Minutes Studying Test Grade

20 65

22 65

25 50

25 52

30 55

30 68

45 70

45 69

60 75

75 80

90 78

90 83

90 85

100 88

100 78

110 95

120 96

120 100

150 91

150 85

160 82

180 80

180 80

Mrs. Blair believes there is a relationship between the number of minutes students study and their test grades. She asked her historyclass to list the number of minutes they studied and their test grade. Using the information provided draw a scatterplot.

What test grade might a student expect if they studied approximately 95 minutes?

X + Y

A) 60

B) 80

C) 100

D) 120

Explanation:A student could expect to earn about an 80 Looking at a scatterplot go along the x-axis until you get to 95 and then find anapproximate y-value associated with that.





25)

x 0 3 4 5 12

y 8 2 6 9 12

For the data in the table, find the line of best fit, rounding values to three places if necessary.

A) y = 4.88 + 0.625x

B) y = 4.98 + 0.725x

C) y = 4.88 + 0.525x

D) y = 4.98 + 0.425x

Explanation:y = 4.88 + 0.525x is correct. Use a stats calculator or software to do the computation.

26)

Hours (x) 0 1 2 3 4 5

Number of Bacteria (y) 23 53 123 282 650 1,493

The table shows the growth of a type of bacteria. Rounded to the nearest tenth, which equation best models this data?

A) y = 266x - 227

B) y = (23)(2.3)x

C) y = (2.3)(23)x

D) y = 93x2 - 2.037x + 86

Explanation:You first have to notice this data is exponential. Data involving bacteria often is. Enter the data into your graphing calculator. Thensolve for "ExpReg". On a TI-83, this can be found using the STAT button.

y = (23)(2.3)x

27)

Year Speed

1 38

2 46

3 52

4 57

5 61

The speed with which an object in space is moving away from the earth is increasing as shown in the table, where speed is given inthousands of miles per hour. Find a logarithmic regression curve to model this data.

A) y = 9.2ln(x) + 44.1

B) y = 10.8ln(x) + 29.9

C) y = 14.2ln(x) + 37.2

D) y = 16.3ln(x) + 18.5

Explanation:y = 14.2ln(x) + 37.2 is correct. Use a graphing calculator to find the equation.



28) Matt studies whether or not the amount of time students study for a test and the grade on the test are related. He determinesfrom his investigation that a student will get a higher grade if they study between 40 and 60 minutes. Which scatterplot matches hisresult?

A)

B)

C)



D)

Explanation:A shows the correct relationship. If studying between 40 and 60 minutes gets the highest grades then on the scatterplot the highesty-values should occur when x is between 40 and 60.

29)

Days People

1 26

2 30

3 34

4 38

5 42

6 46

Allie is trying to get her classmates to sign up to volunteer at the school carnival. The number of people that had signed up by eachday is indicated in the chart. Which line BEST fits the data in the chart?

A) y = 4x - 30

B) y = 4x + 30

C) y = 4x - 22

D) y = 4x + 22

Explanation:Using two points, we find the slope to be 4. We then plug it into point-slope form and solve for y. The line of best fit is y = 4x + 22.

30)



The scatterplot shows temperature data from Nevada. The line of best fit, in blue, has equation C = 23.72 - 0.007m. For whatelevation does the linear model predict a mean temperature of 15° C? (Round to two decimal places.)

A) 1245.71 meters

B) 1421.42 meters

C) 1645.71 meters

D) 1861.50 meters

Explanation:1245.71 meters is correct. Plug 15 into the equation for C, then solve for m to get the answer.

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chambleems.dekalb.k12.ga.uschambleems.dekalb.k12.ga.us/Downloads/VII-T6-FIT A... · The scatterplot shows the data collected from a survey of 19 ... What type of relationship does