Interpret the slope of the Least Squares Line Equation.

As hours increases by one, income will increase by 31.45.

Income increases by 31.45 with each additional 2 hours worked.

As hours increases by one, income will decrease by 242.3.

Write the linear regression equation for the data set foot length (x) and height (y).

height = 117.99 + 1.878(foot length)

height = 28.39(foot length) + 1.155

What's the appropriate interpretation of the slope of the regression line?

For every additional hour of growth, the logarithm of the culture's weight in grams is predicted to increase by 0.61.

For every additional 0.61 hours of growth, the culture is predicted to weight 1 more gram.

For every additional hour of growth, the culture is predicted to weigh 0.61 more grams.

At the beginning of the experiment, the logarithm of the culture's weight in grams was approximately 0.61 ounces.

For the past two-hundred years population per square feet in a northwest suburb can be modeled using the exponential equation . The scatter plot of the data is shown below. Which of the following statements is true?

Plotting the logarithm of population per square mile against year should be approximately linear.

If an attempt is made at fitting a straight line to the original data, the corresponding residual plot would be approximately linear.

If an attempt is made at fitting a straight line to the original data, the corresponding residual plot would be scattered and show no pattern.

Plotting the logarithm of population per square mile against the logarithm of year should be approximately linear.

Some data were collected on the weight of a male white laboratory rat for the first 25 weeks after its birth. The linear regression equation is: Weight = 100 + 40(Time). Which is the best description of the slope for this regression equation in context of the problem?

The slope is 40 which represents a gain of 40 grams per week.

The slope is 40 which respresents the average starting weight of the rats.

The slope is 40 and represents that is takes 40 weeks to gain 1 gram.

The slope is 100 which represents a gain of 100 grams per week.

The standard error (standard deviation) of the residuals tells us _________

our average error in predicting y

our average error in the correlation

whether we look good in the morning

If the point in the upper right corner of this scatterplot is removed from the data set, then what will happen to the slope(b) of the line of best fit and to the correlation(r) ?

b will decrease, and r will increase

b will increase, and r will decrease

A study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil. The response variable in this study is...

amount of fertilizer applied to the soil.

The following scatterplot describes the relationship between height (in cm) and foot length (also in cm) for 12 randomly selected students from the British Census @ Schools database. Which of the following is the best description of this relationship?

There is a moderately weak, positive linear relationship between height and foot length.

There is some random variation, but otherwise height is directly proportional to foot length.

There is a roughly linear relationship between height and foot length.

The relationship between height and foot length is linear, positive, and very strong.

The point in the upper right hand corner of the scatterplot is

an outlier and an influential point

not an outlier or an influential point

not an outlier but an influential point

an outlier but not an influential point

Data on x = the weight of a pickup truck (pounds) and y = distance (in feet) required for a truck traveling 40 miles per hour to come to a complete stop for 30 trucks was used to fit the least squares regression line y^hat = 26 + 0.05x. Which of the following statements is a correct interpretation of the value 26 in the equation of the regression line?

It is not reasonable to interpret the intercept in this setting because a weight of 0 is outside the range of the data used to fit the regression line.

On average, the stopping distance increases by 26 feet for each 1-pound increase in truck weight.

On average, the truck weight increases by 26 pounds for each additional foot in stopping distance.

Approximately 26% of the variation in the stopping distances can be explained by the linear relationship between stopping distance and truck weight.

Regression Review

Authored by Mary Gregg

Mathematics

9th Grade - University

CCSS covered

Used 2+ times

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30 questions

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MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Which of the following statements is not true of the correlation r between the lengths in inches and weights in pounds of a sample of brook trout?

r must take a value between -1 and 1.

r is measured in inches.

If longer trout tend to also be heavier, then r>0.

r would not change if we measured the lengths of the trout in centimeters instead of inches.

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.8

CCSS.HSS.ID.C.9

MULTIPLE CHOICE QUESTION

1 min • 1 pt

What should a residual plot look like?

Distinct Pattern

Curve

Random with no pattern

A few clumps

Tags

CCSS.HSS.ID.B.6

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Shown is a residual plot. Would a linear regression model of the data be most appropriate?

YES

Tags

CCSS.HSS.ID.B.6

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Describe the correlation in the graph shown.

Strong Negative

Strong Positive

Weak Negative

Weak Positive

Tags

CCSS.HSF-LE.A.1B

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which is the best CONTEXTUAL description of the y - intercept for the linear regression equation of the rats: Weight = 100 + 40(Time)?

The y-intercept is 100, which means the rat is predicted to weigh 100 grams at birth.

The y-intercept is 100, which is where the graph crosses the y-axis.

100 is where the data starts on the y-axis.

The y-intercept is 100, which means at a weight of 0, the rat will take 100 seconds.

Tags

CCSS.HSF.LE.B.5

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Estimate the correlation coefficient for this scatterplot.

r = 0.56

r = -0.56

r = 0.92

r = -0.92

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.8

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The correlation coefficient measures...

whether there is a relationship between two variables.

the strength of the relationship between two quantitative variables.

whether a cause and effect relation exists between two variables.

the strength of the linear relationship between two quantitative variables.

Tags

CCSS.HSF-LE.A.1B

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Regression Review

Which of the following statements is not true of the correlation r between the lengths in inches and weights in pounds of a sample of brook trout?

What should a residual plot look like?

Shown is a residual plot. Would a linear regression model of the data be most appropriate?

Describe the correlation in the graph shown.

Which is the best CONTEXTUAL description of the y - intercept for the linear regression equation of the rats: Weight = 100 + 40(Time)?

Estimate the correlation coefficient for this scatterplot.

The correlation coefficient measures...

Interpret the slope of the Least Squares Line Equation.

Which of the following statements are supported by the scatterplot?I. There is a positive association between height and volume.II. There is an outlier in the plot. III. As the height of a cherry tree increases, the volume of useable lumber it yields increases.

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Which of the following statements are supported by the scatterplot?
I. There is a positive association between height and volume.
II. There is an outlier in the plot.
III. As the height of a cherry tree increases, the volume of useable lumber it yields increases.