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.

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# Brief Explanations: 1. For $ x = 1 $: Given value ($-5.1$) is greater than predicted value ($-5.14$), so the data point is above the line (residual $ 0.04>0 $), so this statement is true. 2. For $ x = 3 $: Given value ($ 1.9 $) is less than predicted value ($ 2.28 $), so residual should be negative, so the statement about positive residual is false. 3. For $ x = 4 $: Residual = Given - Predicted = $ 6.2 - 5.99 = 0.21 $, which is correct, so no subtraction error, the statement is false. 4. For $ x = 2 $: Given value ($-1.3$) is greater than predicted value ($-1.43$), so residual should be positive? Wait, residual is Given - Predicted = $-1.3-(-1.43)=0.13$, but the table has $-0.13$. Wait, no, maybe I mixed up. Wait, residual is $ y_{actual}-y_{predicted} $. For $ x = 2 $, actual $ y=-1.3 $, predicted $ y = -1.43 $. So residual is $-1.3-(-1.43)=0.13$, but the table has $-0.13$. Wait, but the statement says "the residual value for $ x = 2 $ should be a positive number because the given point is above the line of best fit". Since actual $ y (-1.3) $ is above predicted $ y (-1.43) $ (because $-1.3 > -1.43$), residual should be positive. But the table has $-0.13$, which is an error? Wait, no, maybe I miscalculated. Wait, $-1.3 - (-1.43)=0.13$, so the table's residual is wrong, but the statement is about whether it should be positive. Since actual is above predicted, residual (actual - predicted) should be positive. So the statement is true? Wait, no, the table has $-0.13$, but the statement is "should be a positive number because the given point is above the line". So if actual is above predicted, residual is positive. So the statement is true? Wait, but let's check the fifth statement: "The residual value for $ x = 3 $ is negative because the given point is below the line of best fit." Given $ x = 3 $, actual $ y = 1.9 $, predicted $ y = 2.28 $. Since $ 1.9 < 2.28 $, so actual is below predicted, so residual $ 1.9 - 2.28=-0.38 $, which is negative. So this statement is true. Wait, the options are to select three? Wait, no, the question says "Select three options". Wait, let's re - evaluate: Wait, first statement: $ x = 1 $, actual $ y=-5.1 $, predicted $ y=-5.14 $. Since $-5.1 > -5.14$, actual is above predicted, so residual is positive (0.04), so the statement "The data point for $ x = 1 $ is above the line of best fit" is true. Fifth statement: "The residual value for $ x = 3 $ is negative because the given point is below the line of best fit." Actual $ y = 1.9 $, predicted $ y = 2.28 $, so actual is below predicted, residual is negative, so this statement is true. Fourth statement: "The residual value for $ x = 2 $ should be a positive number because the given point is above the line of best fit." Actual $ y=-1.3 $, predicted $ y=-1.43 $. Since $-1.3 > -1.43$, actual is above predicted, so residual (actual - predicted) is $-1.3-(-1.43)=0.13$, which is positive. So the statement is true. Wait, but the table has $-0.13$, which is wrong, but the statement is about what it should be. So the statement is true. Wait, but the question is to select three options. Let's list all: 1. True (x=1 above) 2. False (x=3 residual positive) 3. False (x=4 subtraction error) 4. True (x=2 residual should be positive) 5. True (x=3 residual negative because below) Wait, but the question says "Select three options". So the correct ones are: - The data point for $ x = 1 $ is above the line of best fit. (True) - The residual value for $ x = 2 $ should be a positive number because the given point is above the line of best fit. (True, because actual is above predicted, so residual is positive) - The residual value for $ x = 3 $ is negative because the given point is below the line of best fit. (True) Wait, but earlier I thought the fourth statement was true, the first, fourth, and fifth? Wait, no, let's re - check: 1. $ x = 1 $: actual $ y=-5.1 $, predicted $ y=-5.14 $. Since $-5.1 > -5.14$, actual is above predicted, so residual is positive (0.04), so the statement is true. 2. $ x = 3 $: actual $ y = 1.9 $, predicted $ y = 2.28 $. Since $ 1.9 < 2.28 $, actual is below predicted, so residual is negative (1.9 - 2.28=-0.38), so the statement "residual should be positive" is false. 3. $ x = 4 $: residual = 6.2 - 5.99 = 0.21, which is correct, so no subtraction error, statement is false. 4. $ x = 2 $: actual $ y=-1.3 $, predicted $ y=-1.43 $. Since $-1.3 > -1.43$, actual is above predicted, so residual (actual - predicted) is $-1.3-(-1.43)=0.13$, which is positive. So the statement "should be a positive number because the given point is above the line" is true. 5. $ x = 3 $: actual is below predicted, so residual is negative, statement is true. So the three true statements are: - 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. Wait, but the fourth option's statement: "The residual value for $ x = 2 $ should be a positive number because the given point is above the line of best fit." Since actual $ y (-1.3) $ is above predicted $ y (-1.43) $ (because $-1.3 > -1.43$), residual (actual - predicted) is positive. So the statement is true. The fifth option: "The residual value for $ x = 3 $ is negative because the given point is below the line of best fit." Actual $ y = 1.9 $ is below predicted $ y = 2.28 $ (because $ 1.9 < 2.28 $), so residual (actual - predicted) is negative. So the statement is true. The first option: "The data point for $ x = 1 $ is above the line of best fit." Actual $ y=-5.1 $ is above predicted $ y=-5.14 $ (because $-5.1 > -5.14$), so the statement is true. So these three are true. # 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.

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