Unit 4 Review LSRL, Residuals, & Special Data pts

Estimate the correlation coefficient for this scatterplot.

• r = 0.56

• r = -0.56

• r = 0.92

• r = -0.92

Answer explanation

The scatterplot shows a strong positive linear relationship between the variables, indicating a high correlation. The value r = 0.92 reflects this strong positive correlation, making it the correct choice.

Tags

CCSS.HSS.ID.C.8

What is the formula for the regression line?

• y=mx+b

• y=a+bx

Answer explanation

The correct formula for the regression line is \(\hat{y} = a + bx\). Here, \(\hat{y}\) represents the predicted value, \(a\) is the y-intercept, and \(b\) is the slope of the line.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

• 10 miles

• 0.19 miles

• 617.5 miies

• 500 miles

Answer explanation

To predict the distance traveled after 10 hours, substitute x=10 into the equation: y = -1.79 + 61.93(10) = -1.79 + 619.3 = 617.51 miles. Rounding gives approximately 617.5 miles, which is the correct answer.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSS.ID.C.7

True or False: The least-squares regression line will always pass throught the ordered-pair (mean of x, mean of y).

• True

• False

Answer explanation

True. The least-squares regression line is designed to minimize the sum of the squared differences between observed and predicted values, which ensures it always passes through the point (mean of x, mean of y).

Tags

CCSS.8.SP.A.2

1. In the scatterplot of y versus x shown above, the least squares regression line is superimposed on the plot. Which of the following points has the largest residual?

• A

• B

• C

• D

• E

Answer explanation

The residual for a point is the vertical distance from the point to the regression line. Point A is furthest from the line, indicating it has the largest residual compared to points B, C, D, and E.

Tags

CCSS.HSS.ID.B.6B

A residual...

• the difference between the actual value of y and the value of y predicted by the regression line

• actual y - predicted y

• the difference between the actual value of x and the value of x predicted by the regression line

Answer explanation

A residual measures the difference between the actual value of y and the predicted value from the regression line. This is expressed as actual y - predicted y or mathematically as y - \hat{y}.

Tags

CCSS.HSS.ID.B.6B

_____________________ is the use of a regression line for prediction outside the interval of x values used to obtain the line.

Answer explanation

Extrapolation is the correct term for using a regression line to make predictions beyond the range of the original x values. This can lead to inaccurate predictions since the relationship may not hold outside the observed data.

Tags

CCSS.8.SP.A.3

What should a residual plot look like?

• Distinct Pattern

• Curve

• Random with no pattern

• A few clumps

Answer explanation

A residual plot should show random scatter with no discernible pattern. This indicates that the model's assumptions are met and that the residuals are randomly distributed, confirming a good fit.

Tags

CCSS.HSS.ID.B.6B

The ___________________ measures the percent of the variability in the response variable that is accounted for by the least-squares regression line.

• coefficient of determination

• coefficient of relaxation

Answer explanation

The coefficient of determination, denoted as r², quantifies how much of the variability in the response variable is explained by the regression line. It is a key measure in regression analysis.

Tags

CCSS.HSS.ID.B.6B

You are analyzing a scatter plot that has a negative correlation. What is true of the of the x and y values?

• As x increases, y decreases

• As x increases, y increases

• As x decreases, y decreases

Answer explanation

In a scatter plot with a negative correlation, as x increases, y decreases. This means that higher values of x correspond to lower values of y, confirming the correct choice.

Tags

CCSS.HSF-LE.A.1B