Sophia_Statistics_Unit_4_Milestone 2020
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15 questions were answered correctly.
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1
The t

... [Show More] able below shows the grade and reading level for 5 students.
Grade Reading Level
Student 1 2 6
Student 2 6 14
Student 3 5 12
Student 4 4 10
Student 5 1 4
For grade, the mean is 3.6 and the standard deviation is 2.1.
For reading level, the mean is 9.2 and the standard deviation is 4.1.
Using the formula below or Excel, find the correlation coefficient, r, for this set of students. Answer choices
are rounded to the nearest hundredth.
1.00
0.85
0.710.92
RATIONALE
In order to get the correlation, we can use the formula:
Correlation can be quickly calculated by using Excel. Enter the values and use the function "=CORREL(".
CONCEPT
Correlation
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2
This scatterplot shows the maintenance expense for a truck based on its years of service.The equation for least regression line to this data set is ŷ = 76.82x + 88.56.
What is the predicted value (in dollars) for maintenance expenses when a truck is 7 years old?
$549
$473
$626
$703
RATIONALE
In order to get the predicted maintenance expense when the age of the truck is 7 years, we simply substitute the value
7 in our equation for x. So we can note that:
CONCEPT
Predictions from Best-Fit Lines
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3
Raoul lives in Minneapolis and he is planning his spring break trip. He creates the scatterplot below to assess how
much his trip will cost.Which answer choice correctly indicates the explanatory and response variables for the scatterplot?
Explanatory variable: Distance
Response variable: Cost
Explanatory variable: Minneapolis
Response variable: Miles flown
Explanatory variable: Miles flown
Response variable: Minneapolis
Explanatory variable: Cost
Response variable: Distance
RATIONALE
The explanatory variable is what is along the horizontal axis, which is distance. The response variable is along the
vertical axis, which is cost.
CONCEPT
Explanatory and Response Variables
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4
Which of the following scatterplots shows a correlation affected by an influential point?RATIONALE
An influential point will influence correlation that doesn't lie in the range of the other data. This graphs shows an
outlier that is above the other data and lower in the x-direction.
CONCEPT
Cautions about Correlation
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5
Peter analyzed a set of data with explanatory and response variables x and y.
He concluded the mean and standard deviation for x as 7.8 and 3.70, respectively.
He also concluded the mean and standard deviation for y as 12.2 and 4.15, respectively.
The correlation was found to be 0.964.
Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the
hundredths place.
Slope = -1.08
y-intercept = 3.78
Slope = 1.08
y-intercept = -3.78
Slope = 1.08
y-intercept = 3.78Slope = -1.08
y-intercept = -3.78
RATIONALE
We first want to get the slope. We can use the formula:
To then get the intercept, we can solve for the y-intercept by using the following formula:
y with hat on top equals b subscript 0 plus b subscript 1 x
We know the slope, b subscript 1, and we can use the mean of x and the mean of y for the variables x and
y with hat on top to solve for the y-intercept, b subscript 0.
CONCEPT
Finding the Least-Squares Line
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6
In a study of 30 high school students, researchers found a high correlation, 0.93, between amount of exercise and
weight lost.
Which of the following statements is TRUE?
There is a strong positive linear association between weight loss and exercise, but the researchers have not
proven causation.
The researchers proved that exercise causes weight loss, but only for high school students.
The researchers proved that exercise causes weight loss.
93% of the high school students studied lost weight.
RATIONALERecall that correlation measures the strength and direction of linear association. So r= 0.93 indicates a strong positive
linear association. Recall also, that correlation doesn't imply causation. Causation is a direct change in one variable
causing a change in some outcome.
CONCEPT
Correlation and Causation
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7
For the data plotted in the scatterplot, the r2 value was calculated to be 0.9846.
Which of the following sets of statements is true?
98.5% of the variation in age is explained by a linear relationship with yearly income.
The correlation coefficient, r, is 0.969.
98.5% of the variation in yearly income is explained by a nonlinear relationship with age.
The correlation coefficient, r, is 0.992.
98.5% of the variation in yearly income is explained by a linear relationship with age.The correlation coefficient, r, is 0.992
98.5% of the variation in age is explained by a nonlinear relationship with yearly income.
The correlation coefficient, r, is 0.969.
RATIONALE
The coefficient of determination measures the percent of variation in the outcome, y, explained by the regression. So
a value of 0.9846 tells us the regression with age, x, can explain about 98.5% of the variation in income, y.
We can also note that r = .
CONCEPT
Coefficient of Determination/r^2
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8
A correlation coefficient between average temperature and coat sales is most likely to be __________.
between 1 and 2
between 0 and 1
between 0 and -1
between -1 and -2
RATIONALE
If we note that as temp goes up, we would expect coats to be less necessary, so coat sales would go down. So
correlation should be negative and this would be between 0 and -1.
CONCEPT
Positive and Negative Correlations
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9
Thomas was interested in learning more about the salary of a teacher. He believed as a teacher increases in age, the
annual earnings also increases. The age (in years) is plotted against the earnings (in dollars) as shown below. [Show Less]