Maleia is tracking her running training program. The table gives her 5K run time at the end of each month.
Month: 1, 2, 3, 4, 5, 6 Time (minutes): 44, 40, 38, 36, 34, 33
What is the equation for the line of best fit where x represents the month and y represents the time?
y = 2.14x + 33
y = 2.14x + 45
y = −2.14x + 33
y = −2.14x + 45
The equation for the line of best fit is y = -2.14x + 45.
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.
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.
A set of points is shown on the graph.
Scatter plot with a point at negative 5 comma negative 1, a point at negative 2 comma 4, a point at 1 comma 9, a point at 3 comma 5, and a point at 4 comma 7.
Which of the following equations is the best model for a line of fit for the data?
a. y equals 1 fourth times x plus 5.
b. y equals negative 1 fourth times x plus 5.
c. y equals 3 fourths times x plus.
d. y equals negative 3 fourths times x plus 5.
Based on the given points on the scatter plot, we can see that the best model for a line of fit would be the equation: y = 3/4x + 2. Therefore, option c is the correct answer.
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?
0.09 feet
−0.09 feet
−68.16 feet
68.16 feet
To find the predicted depth of the dive, we substitute t = 6 seconds into the equation ŷ = 5.1 + 10.51t.
ŷ = 5.1 + 10.51(6)
= 5.1 + 63.06
= 68.16
Therefore, the predicted depth of the dive is 68.16 feet. The correct answer is "68.16 feet".
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
Based on the scatter plot, we can see that the relationship between the number of stamps, y, and the number of months, x, is increasing linearly.
If we use the regression line to predict the number of stamps she collected in the 25th month, we would use the equation y = mx + b, where m is the slope and b is the y-intercept.
From the given points on the scatter plot, we can calculate the slope as:
m = (190 - 30) / (5 - 1)
= 160 / 4
= 40
Next, we need to calculate the y-intercept, which can be determined by substituting the values of any point into the equation y = mx + b. Let's use the first point (1,30):
30 = 40(1) + b
b = 30 - 40
b = -10
Now we can substitute x = 25 into the equation y = mx + b to find the approximate predicted number of stamps:
y = 40(25) - 10
= 1000 - 10
= 990
Therefore, the approximate predicted number of stamps Katie collected in the 25th month is 990. The correct answer is "990".
A data set comparing a woman's shoe size to her height is represented by the table.
Shoe Size: 7.5, 9, 11, 7, 9, 10, 12, 13, 13 Height (inches): 63, 72.5, 70, 62, 69.5, 72, 72.5, 73, 70
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