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. B. 0.451
5. 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.