1. Which of the following describes the line of best fit for a set of data?
A. a line that goes through two representative points from the data set
B. a line that goes through every point in the data set
C. a line that fits the whole data set the best
D. a line that has half the points above it and half the points below it
2. Determine the line of best fit to predict y from x for the following data. Round to three decimal places as needed.
x 5 7 8 3 2
y 7 9 9 7 6
(1 point)
A. x=−8.722+1.806y
B. y=0.5+5.1x
C. y=5.1+0.5x
D. y=1.806−8.722x
3. A biology student is investigating the claim that the temperature in Fahrenheit, T, can be predicted by the number of cricket chirps per minute, r. She has collected the data in the table below. Find the equation for the line of best fit. Round to three decimal places as needed.
r 72 73 76 92 115 130 131 141
T 55 58 54 62 64 71 70 69
A. T=39.6+0.225r
B. T=0.225+39.6r
C. r=4.066−151.9T
D. r=−151.9+4.066T
4. Use the least squares method to find the slope of the line of best fit for the data set below. Round to three decimal places.
x −6 −4 −1 4 5
y 11 9 2 −7 -9
A. −0.531
B. 0.451
C. −1.873
D. 0.237
5. Barrett used the least squares method for the following data set and says that the slope of the line of best fit is −0.236. Wallace, without looking at Barrett's work or performing any calculations, says that Barrett's answer is wrong. How does Wallace know that Barrett is incorrect?
d 0.1 0.2 0.8 1.2 1.5 2.4 3.1 3.1
s 14 10 35 48 57 84 110 108
A. From the table, it is clear that the s-intercept would be positive. Barrett's line would have a negative intercept because the slope is negative.
B. From the table, it can be seen that there is a positive relationship, so the slope of the line of best fit must be positive.
C. The data in the table has an exponential relationship, so there would not be a line of best fit.
D. The data in the table has a quadratic relationship, so there would not be a line of best fit.
1. C. a line that fits the whole data set the best.
2. C. y=5.1+0.5x
3. A. T=39.6+0.225r
4. A. −0.531
5. B. From the table, it can be seen that there is a positive relationship, so the slope of the line of best fit must be positive. Since Barrett's answer has a negative slope, it is incorrect.
thx
1. C. a line that fits the whole data set the best
2. C. y=5.1+0.5x
3. A. T=39.6+0.225r
4. B. 0.451
5. B. From the table, it can be seen that there is a positive relationship, so the slope of the line of best fit must be positive.
1. The line of best fit for a set of data is the line that best represents the relationship between the independent variable (x) and the dependent variable (y). It is an approximation of the data points and is used to make predictions or analyze trends.
The correct answer is C. A line of best fit is the line that fits the whole data set the best. It may not necessarily pass through every point or have an equal number of points above and below it.
2. To determine the line of best fit, we can use linear regression. Linear regression calculates the equation of a line that represents the relationship between x and y.
Using a calculator or software that performs linear regression analysis, we can input the given x and y values to obtain the equation of the line of best fit.
The correct answer is C. y = 5.1 + 0.5x.
3. Similar to question 2, we can use linear regression to find the equation for the line of best fit.
Inputting the given values for r and T into a linear regression analysis, we can obtain the equation of the line of best fit.
The correct answer is A. T = 39.6 + 0.225r.
4. To find the slope of the line of best fit using the least squares method, we can input the given x and y values into a calculator or software that performs linear regression analysis.
The correct answer is C. The slope of the line of best fit is -1.873.
5. Wallace can determine that Barrett's answer is incorrect because the given data shows a positive relationship between d and s.
Therefore, the correct answer is B. From the table, it can be seen that there is a positive relationship, so the slope of the line of best fit must be positive. Since Barrett provided a negative value for the slope, his answer is incorrect.