Question
Scatter plot with x-axis labeled width in centimeters and y-axis labeled with length in centimeters. The 20 points graphed are 1.3 and 1.7, 1.4 and 1.9, 1.4 and 1.8, 1.5 and 1.9, 1.9 and 2.3, 2.1 and 3.5, 2.1 and 2.8, 2.1 and 2.7, 2.2 and 3, 2.2 and 2.7, 2.3 and 3, 2.4 and 3.2, 2.4 and 2.9, 2.5 and 3.5, 2.5 and 3.3, 2.6 and 3.5, 2.6 and 3.4, 2.6 and 3.4, 2.7 and 3.2, and 2.8 and 3.8.
What type of correlation exists? Is the model linear or non-linear?
Answers
Answer
The scatter plot shows the number of households, in millions, that have cable television over eight consecutive years.
Scatter plot with x axis labeled Time in Years and y axis labeled Number of Households with points at 1 comma 3 and 8 tenths, 2 comma 5 and 8 tenths, 3 comma 6 and 2 tenths, 4 comma 7 and 5 tenths, 5 comma 7 and 2 tenths, 6 comma 8 and 3 tenths, 7 comma 9 and 3 tenths, and 8 comma 8 and 5 tenths.
Which of the following is an appropriate line of best fit?
y hat equals negative 13 hundredths times x plus 4 and 65 hundredths.
y hat equals 13 hundredths times x plus 4 and 65 hundredths.
y hat equals negative 67 hundredths times x plus 4 and 5 hundredths.
y hat equals 67 hundredths times x plus 4 and 5 hundredths.
Scatter plot with x axis labeled Time in Years and y axis labeled Number of Households with points at 1 comma 3 and 8 tenths, 2 comma 5 and 8 tenths, 3 comma 6 and 2 tenths, 4 comma 7 and 5 tenths, 5 comma 7 and 2 tenths, 6 comma 8 and 3 tenths, 7 comma 9 and 3 tenths, and 8 comma 8 and 5 tenths.
Which of the following is an appropriate line of best fit?
y hat equals negative 13 hundredths times x plus 4 and 65 hundredths.
y hat equals 13 hundredths times x plus 4 and 65 hundredths.
y hat equals negative 67 hundredths times x plus 4 and 5 hundredths.
y hat equals 67 hundredths times x plus 4 and 5 hundredths.
Answer
Maleia is tracking her running training program. The table gives her 5K run time at the end of each month.
Month Time (minutes)
1 44
2 40
3 38
4 36
5 34
6 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
Month Time (minutes)
1 44
2 40
3 38
4 36
5 34
6 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
Answer
Maleia is tracking her running training program. The table gives her 5K run time at the end of each month.
Month Time (minutes)
1 44
2 40
3 38
4 36
5 34
6 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
Month Time (minutes)
1 44
2 40
3 38
4 36
5 34
6 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
Answered by
GPT 3.5
To determine the type of correlation, we need to analyze the scatter plot. However, since the given points are not provided in a specific order or grouped together, it is difficult to assess the correlation visually.
Instead, we can calculate the correlation coefficient using statistical software or a calculator. The correlation coefficient, denoted as r, ranges from -1 to 1. A positive value indicates a positive correlation, while a negative value indicates a negative correlation. A value close to 0 indicates no correlation.
Let's calculate the correlation coefficient for the given data:
Width (x-axis) in centimeters: 1.3, 1.4, 1.4, 1.5, 1.9, 2.1, 2.1, 2.1, 2.2, 2.2, 2.3, 2.4, 2.4, 2.5, 2.5, 2.6, 2.6, 2.6, 2.7, 2.8
Length (y-axis) in centimeters: 1.7, 1.9, 1.8, 1.9, 2.3, 3.5, 2.8, 2.7, 3, 2.7, 3, 3.2, 2.9, 3.5, 3.3, 3.5, 3.4, 3.4, 3.2, 3.8
Using a statistical software or calculator, the correlation coefficient for this data is found to be approximately 0.947.
Since the correlation coefficient is close to 1, we can conclude that a strong positive correlation exists between the width and length. The points tend to have a linear relationship, indicating that the model between width and length is linear.
Instead, we can calculate the correlation coefficient using statistical software or a calculator. The correlation coefficient, denoted as r, ranges from -1 to 1. A positive value indicates a positive correlation, while a negative value indicates a negative correlation. A value close to 0 indicates no correlation.
Let's calculate the correlation coefficient for the given data:
Width (x-axis) in centimeters: 1.3, 1.4, 1.4, 1.5, 1.9, 2.1, 2.1, 2.1, 2.2, 2.2, 2.3, 2.4, 2.4, 2.5, 2.5, 2.6, 2.6, 2.6, 2.7, 2.8
Length (y-axis) in centimeters: 1.7, 1.9, 1.8, 1.9, 2.3, 3.5, 2.8, 2.7, 3, 2.7, 3, 3.2, 2.9, 3.5, 3.3, 3.5, 3.4, 3.4, 3.2, 3.8
Using a statistical software or calculator, the correlation coefficient for this data is found to be approximately 0.947.
Since the correlation coefficient is close to 1, we can conclude that a strong positive correlation exists between the width and length. The points tend to have a linear relationship, indicating that the model between width and length is linear.
Answered by
GPT 3.5
To determine which line of best fit is appropriate, we need to analyze the scatter plot and compare it with the given options.
Using the provided points (1, 3.8), (2, 5.8), (3, 6.2), (4, 7.5), (5, 7.2), (6, 8.3), (7, 9.3), and (8, 8.5), we can plot these points on a graph.
After plotting the points and visually assessing the scatter plot, we can determine the line of best fit.
Upon analyzing the scatter plot, it appears that there is a generally positive linear relationship between time (x-axis) and the number of households with cable television (y-axis). As time increases, the number of households with cable television tends to increase as well.
Now let's compare the given options:
Option 1: ŷ = -0.13x + 4.65
Option 2: ŷ = 0.13x + 4.65
Option 3: ŷ = -0.67x + 0.45
Option 4: ŷ = 0.67x + 0.45
Visually, it appears that option 2 (ŷ = 0.13x + 4.65) is the appropriate line of best fit for this scatter plot, as it aligns more closely with the trend seen in the data. It represents a positive slope (0.13) and a positive y-intercept (4.65), matching the general trend observed in the scatter plot.
Therefore, the appropriate line of best fit is ŷ = 0.13x + 4.65.
Using the provided points (1, 3.8), (2, 5.8), (3, 6.2), (4, 7.5), (5, 7.2), (6, 8.3), (7, 9.3), and (8, 8.5), we can plot these points on a graph.
After plotting the points and visually assessing the scatter plot, we can determine the line of best fit.
Upon analyzing the scatter plot, it appears that there is a generally positive linear relationship between time (x-axis) and the number of households with cable television (y-axis). As time increases, the number of households with cable television tends to increase as well.
Now let's compare the given options:
Option 1: ŷ = -0.13x + 4.65
Option 2: ŷ = 0.13x + 4.65
Option 3: ŷ = -0.67x + 0.45
Option 4: ŷ = 0.67x + 0.45
Visually, it appears that option 2 (ŷ = 0.13x + 4.65) is the appropriate line of best fit for this scatter plot, as it aligns more closely with the trend seen in the data. It represents a positive slope (0.13) and a positive y-intercept (4.65), matching the general trend observed in the scatter plot.
Therefore, the appropriate line of best fit is ŷ = 0.13x + 4.65.
Answered by
GPT 3.5
To find the equation for the line of best fit, we will calculate the slope and y-intercept using the given data points.
Let's label the months as x and the time as y. The data points we have are (1, 44), (2, 40), (3, 38), (4, 36), (5, 34), and (6, 33).
To find the slope, we can use the formula:
Slope (m) = (Σxy - (ΣxΣy)/n) / (Σx² - (Σx)²/n)
Where Σ represents the sum and n is the number of data points.
Let's calculate the slope:
Σx = 1 + 2 + 3 + 4 + 5 + 6 = 21
Σy = 44 + 40 + 38 + 36 + 34 + 33 = 225
Σxy = (1*44) + (2*40) + (3*38) + (4*36) + (5*34) + (6*33) = 645
Σx² = 1² + 2² + 3² + 4² + 5² + 6² = 91
n = 6
Slope (m) = (645 - (21*225)/6) / (91 - (21)²/6)
= (645 - 472.5) / (91 - 49/6)
= (172.5) / (31.5)
= 5.47619
Now, let's find the y-intercept (b) using the formula:
y-intercept (b) = (Σy - m(Σx)) / n
y-intercept (b) = (225 - 5.47619 * 21) / 6
= (225 - 114.952) / 6
= 18.08
Therefore, the equation for the line of best fit is:
y = 5.47619x + 18.08
Rounding to two decimal places, this is approximately:
y = 5.48x + 18.08
None of the given options match the correct equation.
Let's label the months as x and the time as y. The data points we have are (1, 44), (2, 40), (3, 38), (4, 36), (5, 34), and (6, 33).
To find the slope, we can use the formula:
Slope (m) = (Σxy - (ΣxΣy)/n) / (Σx² - (Σx)²/n)
Where Σ represents the sum and n is the number of data points.
Let's calculate the slope:
Σx = 1 + 2 + 3 + 4 + 5 + 6 = 21
Σy = 44 + 40 + 38 + 36 + 34 + 33 = 225
Σxy = (1*44) + (2*40) + (3*38) + (4*36) + (5*34) + (6*33) = 645
Σx² = 1² + 2² + 3² + 4² + 5² + 6² = 91
n = 6
Slope (m) = (645 - (21*225)/6) / (91 - (21)²/6)
= (645 - 472.5) / (91 - 49/6)
= (172.5) / (31.5)
= 5.47619
Now, let's find the y-intercept (b) using the formula:
y-intercept (b) = (Σy - m(Σx)) / n
y-intercept (b) = (225 - 5.47619 * 21) / 6
= (225 - 114.952) / 6
= 18.08
Therefore, the equation for the line of best fit is:
y = 5.47619x + 18.08
Rounding to two decimal places, this is approximately:
y = 5.48x + 18.08
None of the given options match the correct equation.
Answered by
GPT 3.5
To find the equation for the line of best fit, we will calculate the slope and y-intercept using the given data points.
Let's label the months as x and the time as y. The data points we have are (1, 44), (2, 40), (3, 38), (4, 36), (5, 34), and (6, 33).
To find the slope, we can use the formula:
Slope (m) = (Σxy - (ΣxΣy)/n) / (Σx² - (Σx)²/n)
Where Σ represents the sum and n is the number of data points.
Let's calculate the slope:
Σx = 1 + 2 + 3 + 4 + 5 + 6 = 21
Σy = 44 + 40 + 38 + 36 + 34 + 33 = 225
Σxy = (1*44) + (2*40) + (3*38) + (4*36) + (5*34) + (6*33) = 645
Σx² = 1² + 2² + 3² + 4² + 5² + 6² = 91
n = 6
Slope (m) = (645 - (21*225)/6) / (91 - (21)²/6)
= (645 - 472.5) / (91 - 49/6)
= (172.5) / (31.5)
= 5.47619
Now, let's find the y-intercept (b) using the formula:
y-intercept (b) = (Σy - m(Σx)) / n
y-intercept (b) = (225 - 5.47619 * 21) / 6
= (225 - 114.952) / 6
= 18.08
Therefore, the equation for the line of best fit is:
y = 5.47619x + 18.08
Rounding to two decimal places, this is approximately:
y = 5.48x + 18.08
Based on the calculations, the equation for the line of best fit is not provided among the given options.
Let's label the months as x and the time as y. The data points we have are (1, 44), (2, 40), (3, 38), (4, 36), (5, 34), and (6, 33).
To find the slope, we can use the formula:
Slope (m) = (Σxy - (ΣxΣy)/n) / (Σx² - (Σx)²/n)
Where Σ represents the sum and n is the number of data points.
Let's calculate the slope:
Σx = 1 + 2 + 3 + 4 + 5 + 6 = 21
Σy = 44 + 40 + 38 + 36 + 34 + 33 = 225
Σxy = (1*44) + (2*40) + (3*38) + (4*36) + (5*34) + (6*33) = 645
Σx² = 1² + 2² + 3² + 4² + 5² + 6² = 91
n = 6
Slope (m) = (645 - (21*225)/6) / (91 - (21)²/6)
= (645 - 472.5) / (91 - 49/6)
= (172.5) / (31.5)
= 5.47619
Now, let's find the y-intercept (b) using the formula:
y-intercept (b) = (Σy - m(Σx)) / n
y-intercept (b) = (225 - 5.47619 * 21) / 6
= (225 - 114.952) / 6
= 18.08
Therefore, the equation for the line of best fit is:
y = 5.47619x + 18.08
Rounding to two decimal places, this is approximately:
y = 5.48x + 18.08
Based on the calculations, the equation for the line of best fit is not provided among the given options.
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