STATISTICS MISC
UNIT 4 – MILESTONE 4
You passed this milestone
Jesse takes two data points from the weight and feed cost data set to calcu... [Show More] late a slope, or average rate of change. A hamster weighs half a pound and costs $2 per week to feed, while a Labrador Retriever weighs 62.5 pounds and costs $10 per week to feed.
Using weight as the explanatory variable, what is the slope of a line between these two points? Answer choices are rounded to the nearest hundredth.
$4.00 / lb.
$6.25 / lb.
$0.13 / lb.
$7.75 / lb.
RATIONALE
In order to get slope, we can use the formula: .
Using the information provided, the two points are: (0.5 lb., $2) and (62.5 lb., $10). We can note that:
CONCEPT
Linear Equation Algebra Review 2
Brad reads a scatterplot that displays the relationship between the number of cars owned per household and the average number of citizens who have health insurance in neighborhoods across the country. The plot shows a strong positive correlation.
Brad recalls that correlation does not imply causation. In this example, Brad sees that increasing the number of cars per household would not cause members of his community to purchase health insurance.
Identify the lurking variable that is causing an increase in both the number of cars owned and the average number of citizens with health insurance.
The number of different car brands
The number of citizens in the United States who do not have health insurance
Average health insurance costs in the United States
Average annual salary per household
RATIONALE
Recall that a lurking variable is something that must be related to the outcome and explanatory variable that when considered can help explain a relationship between 2 variables. Since higher income is positively related to owning more cars and having health insurance, this variable would help explain why we see this association.
CONCEPT
Correlation and Causation 3
Two bags each contain tickets numbered 1 to 10. John draws a ticket from each bag five times, replacing the tickets after each draw. He records the number on the ticket for each draw from both the bags:
Bag 1 Bag 2
Draw 1 2 4
Draw 2 4 5
Draw 3 1 3
Draw 4 6 4
Draw 5 7 9
For the the first bag, the mean is 4 and the standard deviation is 2.5. For the second bag, the mean is 5 and the standard deviation is 2.3.
Using the formula below or Excel, find the correlation coefficient, r, for this set of tickets John drew. Answer choices are rounded to the nearest hundredth.
0.75
0.70
0.50
0.56
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 4
Shawna finds a study of American women that has an equation to predict weight (in pounds) from height (in inches): ŷ = -260 + 6.6x. Shawna's mom’s height is 68 inches and her weight is 179 pounds.
What is the residual of weight and height for Shawna's mom?
9.8 pounds
-9.8 pounds
188.8 pounds
921.4 pounds
RATIONALE
Recall that to get the residual, we take the actual value - predicted value. So if the actual height of 68 inches and the resulting actual weight is 179 pounds, we simply need the predicted weight. Using the regression line, we can say:
The predicted weight is 188.8 pounds. So the residual is:
CONCEPT
Residuals 5
Data for price and thickness of soap is entered into a statistics software package and results in a regression equation of ŷ = 0.4 + 0.2x.
What is the correct interpretation of the slope if the price is the response variable and the thickness is an explanatory variable?
The price of the soap increases by $0.40, on average, when the thickness increases by 1 cm.
The price of the soap increases by $0.20, on average, when the thickness increases by 1 cm.
The price of the soap decreases by $0.20, on average, when the thickness increases by 1 cm.
The price of the soap decreases by $0.40, on average, when the thickness increases by 1 cm.
RATIONALE
When interpreting the linear slope, we generally substitute in a value of 1. So we can note that, in general, as x increases by 1 unit the slope tells us how the outcome changes. So for this equation we can note as x (thickness) increases by 1 cm, the outcome (price) will increase by $0.20 on average.
CONCEPT
Interpreting Intercept and Slope 6
Which of the following scatterplots shows an outlier in the y-direction?
RATIONALE
To have an outlier in the y-direction the outlier must be in the range of x data but outside the range of y-data. This outlier is outside of the data in the y direction, lying below all of the data.
CONCEPT
Outliers and Influential Points 7
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.
Using the best-fit line, approximately how much money would a 45-year-old teacher make?
$50,000
$55,000
$58,000
$48,000
RATIONALE
To get a rough estimate of the salary of a 45 year-old, we go to the value of 45 on the horizontal axis and then see where it falls on the best-fit line. This looks to be about $50,000.
CONCEPT
Best-Fit Line and Regression Line 8
For ten students, a teacher records the following scores of two assessments, Quiz 1 and Test.
Quiz 1 (x) Test (y)
15 20
12 15
10 12
14 18
10 10
8 13
6 12
15 10
16 18
13 15
Mean 11.9 14.3
Standard Deviation 3.3 3.5
The correlation of Quiz 1 and Test is 0.568.
Given the information below, what is the slope and y-intercept for the least-squares line of the Quiz 1 scores and Test scores? Answer choices are rounded to the hundredths place.
Slope = 0.60
y-intercept = 1.22
Slope = 0.54
y-intercept = 1.22
Slope = 0.54
y-intercept = 1.71
Slope = 0.60
y-intercept = 7.16
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:
We know the slope, , and we can use the mean of x and the mean of y for the variables and to solve for the y-intercept, .
CONCEPT
Finding the Least-Squares Line 9
A bank manager declares, with help of a scatterplot, that the number of health insurances sold may have some association with the number of inches it snows.
How many policies were sold when it snowed 2 to 4 inches?
210
350
240
470
RATIONALE
In order to find the total number of policies between 2 and 4 inches, we must add the three values of 10 in that interval.
At 2 inches, there were 100 policies. At 3 inches, there were 110 policies. At 4 inches, there were 140 policies.
So the total is 100 + 110 + 140 = 350 policies.
CONCEPT
Scatterplot 10
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?
$473
$549
$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 11
This scatterplot shows the performance of an electric motor using the variables speed of rotation and voltage.
Select the answer choice that accurately describes the data's form, direction, and strength in the scatterplot.
Form: The data points are arranged in a curved line.
Direction: The speed of rotation increases with an increase in voltage. Strength: The data points are far apart from each other.
Form: The data points appear to be in a straight line.
Direction: The speed of rotation increases with an increase in voltage. Strength: The data points are closely concentrated.
Form: The data points are arranged in a curved line.
Direction: The voltage increases as the speed of rotation increases. Strength: The data points are far apart from each other.
Form: The data points appear to be in a straight line.
Direction: The voltage increases as the speed of rotation increases. Strength: The data points are closely concentrated.
RATIONALE
If we look at the data, it looks as if a straight line captures the relationship, so the form is linear. The slope of the line is positive, so it is increasing. Finally, since the dots are closely huddled around each other in a linear fashion, it looks strong.
CONCEPT
Describing Scatterplots 12
John, the owner of an ice-cream parlor, collects data for the daily sales of ice cream with respect to the daily temperature.
If John were to create a scatterplot, all of the following will be characteristics of correlation EXCEPT
.
Amount of daily sales at any given temperature
Degree of association between the daily sales and temperature
Strength of association between the daily sales and temperature
Direction of association between the daily sales and temperature [Show Less]
