Question

fiona wrote the predicted and residual values for a data set using the line of best fit y = 3.71x - 8.85. which statements are true about the table? select three options. the data point for x = 1 is above the line of best fit. the residual value for x = 3 should be a positive number because the data point is above the line of best fit. fiona made a subtraction error when she computed the residual value for x = 4. the residual value for x = 2 should be a positive number because the given point is above the line of best fit. the residual value for x = 3 is negative because the given point is below the line of best fit.

Explanation:

Step1: Recall the formula for residual

The formula for residual is \(Residual = Given - Predicted\). If the residual is positive, the data point is above the line of best fit. If the residual is negative, the data point is below the line of best fit.

Step2: Analyze each option

• For \(x = 1\):

Given \(y=-5.1\), predicted \(y = - 5.14\). Residual \(=-5.1-(-5.14)=0.04>0\). So the data point for \(x = 1\) is above the line of best fit.

• For \(x = 3\):

Given \(y = 1.9\), predicted \(y=2.28\). Residual \(=1.9 - 2.28=-0.38<0\). Since residual is negative, the data point is below the line of best fit.

• For \(x = 4\):

Given \(y = 6.2\), predicted \(y=5.99\). Residual \(=6.2-5.99 = 0.21\). There is no subtraction error.

• For \(x = 2\):

Given \(y=-1.3\), predicted \(y=-1.43\). Residual \(=-1.3-(-1.43)=0.13>0\). The residual value for \(x = 2\) should be a positive number because the given point is above the line of best fit. But in the table, it is \(-0.13\) (wrong).

• For \(x = 3\) (re - check):

Since \(Residual=Given - Predicted=1.9 - 2.28=-0.38\), the residual value for \(x = 3\) is negative because the given point is below the line of best fit.

Answer:

The data point for \(x = 1\) is above the line of best fit; The residual value for \(x = 2\) should be a positive number because the given point is above the line of best fit; The residual value for \(x = 3\) is negative because the given point is below the line of best fit.