The scatter plot shows the winning times, in seconds, in a 50-meter race over eight consecutive years.
Scatter plot with x axis labeled Time in Years and y axis labeled Winning Time with points at 1 comma 5 and 4 tenths, 2 comma 5, 3 comma 4 and 6 tenths, 4 comma 4 and 9 tenths, 5 comma 4 and 1 tenth, 6 comma 3 and 9 tenths, 7 comma 3 and 6 tenths, and 8 comma 3 and 3 tenths.
Which of the following is an appropriate line of best fit?
y hat equals negative 29 hundredths times x plus 5 and 67 hundredths.
y hat equals 29 hundredths times x plus 5 and 67 hundredths.
y hat equals negative 45 hundredths times x plus 7 and 69 hundredths.
y hat equals 45 hundredths times x plus 7 and 69 hundredths.
Question 2(Multiple Choice Worth 1 points)
(04.05 MC)
A data set comparing a woman's shoe size to her height is represented by the table.
What is the equation for the line of best fit for a woman's height, y, based on her shoe size, x?
y = 1.24x + 70.1
y = −1.24x − 70.1
y = 1.36x + 55.6
y = −1.36x − 55.6
Question 3(Multiple Choice Worth 1 points)
(04.05 MC)
Maleia is tracking her running training program. The table gives her 5K run time at the end of each month.
What is the equation for the line of best fit where x represents the month and y represents the time?
y = −2.78x + 33.6
y = −2.78x + 48.5
y = 2.78x + 33.6
y = 2.78x + 48.5
Question 4(Multiple Choice Worth 1 points)
(04.05 MC)
The table compares the average daily temperature and ice cream sales each day.
What is the slope of the line of best fit, where x represents the average daily temperature and y represents the total ice cream sales? (Round your answer to one decimal place.)
1.8
2.3
3.1
4.3
Question 5(Multiple Choice Worth 1 points)
(04.05 MC)
The depth at which sharks dive, y, in feet, as related to the duration of the dive, t, in seconds, is represented by the linear model ŷ = 5.1 + 10.51t.
If the dive duration is 6 seconds, what is the predicted depth of the dive?
A company determines an employee's starting salary according to the number of years of experience, as detailed in the table.
Years of experience Salary
0 $40,000
1 $42,150
2 $44,260
3 $46,785
4 $48,820
5 $51,126
Use the equation for the line of best fit to predict the salary for an employee with 7 years of experience? (Round your answer to the nearest dollar.)
$52,900
$53,340
$53,914
$55,573
Question 7(Multiple Choice Worth 1 points)
(04.05 LC)
A set of points is shown on the graph.
Scatter plot with a point at negative 5 comma negative 1, a point at 1 comma 4, a point at 3 comma 2, a point at 5 comma 4, and a point at 6 comma 7.
Which of the following equations is the best model for a line of fit for the data?
y equals 2 thirds times x plus 2
y equals negative 2 thirds times x plus 2
y equals 1 third times x plus 2
y equals negative 1 third ties x minus 2
Question 8(Multiple Choice Worth 1 points)
(04.05 LC)
The graph shows a scatter plot for a set of data.
Scatter plot with x-axis labeled year and y-axis labeled megawatts. The 18 points plotted are 1982 and 76.2, 1983 and 50.6, 1984 and 46.4, 1985 and 35.5, 1986 and 31.1, 1987 and 26.1, 1988 and 21, 1989 and 15.6, 1990 and 14.9, 1991 and 13.8, 1992 and 13, 1993 and 13, 1994 and 10, 1995 and 10, 1996 and 7, 1997 and 6.9, 1998 and 6.6, and 1999 and 6.
What type of correlation exists? Is the model linear or non-linear?
The graph shows a negative correlation, and it is a linear model.
The graph shows a positive correlation, and it is a linear model.
The graph shows a negative correlation, and it is a non-linear model.
The graph shows a positive correlation, and it is a non-linear model.
Question 9(Multiple Choice Worth 1 points)
(04.05 MC)
Data were collected on the distance a golf ball will travel when hit by a golf club at a certain speed. The speed, s, is measured in miles per hour, and distance, y, is measured in yards. The regression line is given by ŷ = 5.32 + 46.73s.
Identify the slope and y-intercept of the regression line. Interpret each value in context.
The slope, 5.32, indicates that the distance increases by 5.32 yards for every one mile per hour of speed. The y-intercept, 46.73, is the distance estimated by this model if the speed is zero miles per hour.
The slope, 5.32, indicates that the distance decreases by 5.32 yards for every one mile per hour of speed. The y-intercept, 46.73, is the distance estimated by this model if the speed is one mile per hour.
The slope, 46.73, indicates that the distance increases by 46.73 yards for every one mile per hour of speed. The y-intercept, 5.32, is the distance estimated by this model if the speed is zero miles per hour.
The slope, 46.73, indicates that the distance decreases by 46.73 yards for every one mile per hour of speed. The y-intercept, 5.32, is the distance estimated by this model if the speed is one mile per hour.
Question 10(Multiple Choice Worth 1 points)
(04.05 MC)
The scatter plot shows the number of stamps Katie collected in different months:
Scatter plot with Months on x axis and Number of Stamps on y axis with points at 1 comma 30, 2 comma 70, 3 comma 110, 4 comma 150, and 5 comma 190.
What is the approximate predicted number of stamps she collected in the 25th month?
980
990
1,000
1,010
1 answer
Here are the answers to your questions based on the information provided:
Question 1: The equation showing a negative slope, which is usually appropriate for a decline in winning times, is likely correct based on the context of the data. The appropriate line of best fit is:
y hat equals negative 29 hundredths times x plus 5 and 67 hundredths.
Question 2: The equation for women's height based on shoe size should have a positive slope if taller women wear larger shoes. The appropriate equation is likely:
y = 1.24x + 70.1 (assuming this estimates height based on increasing shoe size).
Question 3: Since Maleia's 5K run times are decreasing, the equation representing this trend should have a negative slope:
y = −2.78x + 48.5.
Question 4: To find the slope of the line of best fit for temperature versus ice cream sales, we would analyze the trend from the data given, and based on the context, the likely answer is:
2.3.
Question 5: To predict the depth at a dive duration of 6 seconds with the model given:
ŷ = 5.1 + 10.51(6) = 5.1 + 63.06 = 68.16 feet.
Thus, the answer is 68.16 feet.
Question 6: Assuming a linear relationship, using the slope derived from the data, we'll calculate:
If we apply the same trend for 7 years of experience, the nearest salary predicted is likely:
$53,914.
Question 7: Observing the scatter plot points, the best model based on the upward trend is likely to have a positive slope:
y equals 2 thirds times x plus 2.
Question 8: The given scatter plot data, showing a decline in measurements over years indicates:
The graph shows a negative correlation, and it is a linear model.
Question 9: For the regression line provided, the correct interpretations are:
The slope, 46.73, indicates that the distance increases by 46.73 yards for every one mile per hour of speed. The y-intercept, 5.32, is the distance estimated by this model if the speed is zero miles per hour.
Question 10: By analyzing the trend of the stamps collected over the months and using a linear extrapolation method:
The approximate predicted number of stamps collected in the 25th month is:
1,010.
These solutions should assist you in answering the questions accurately.
