Chapter 15
In the two plots shown, the regression line in Plot A will have the ________ slope.
larger
Which regression line will give the most useful predictions?
y = 5.8 + 0.15x, r2 = 0.9
The general form for a linear equation is given as: y = a + bx. In the equation, _______ tells us about how y changes when x changes. (Enter the letter of the variable.)
b
A college professor investigated the relationship between the number of absences and the final grade for the course. He found that more absences were associated with lower final grades. Number of absences explained 25% of the variation is final grades. The correlation coefficient for this relationship will be ______.
-.5
A plot of weights and lengths of alligators is given in the following scatterplot. This plot indicates that a gator measuring about 115 inches in length weighed about _____ pounds.
200
Edwin Hubble collected data from 24 galaxies measuring the distance a galaxy is from Earth (x) and the velocity with which it appears to be receding (y) to investigate if there was a linear relationship between the two variables. Based on the information in the table, the slope is ________.
454.16
Data were recorded on a simple random sample of elementary school children. Researchers reported a correlation of r = -0.79 between the time spent watching TV (x) and hours spent on homework (y). Which of the following is a correct conclusion about this value of r?
A strong negative association exists between time spent watching TV and time spent doing homework.
In the following scatterplot x = number of Methodist ministers per year is plotted against y = number of barrels of rum imported for the same year. Data was collected every ten years in Boston. Why is the correlation (r = +1.0) so high?
Because increase in population of Boston is a lurking variable.
Researchers interviewed a group of women with knee pain awaiting knee replacement surgery. They also interviewed a group of women from the same geographical area with no knee pain. These researchers reported that wearing high-heeled shoes caused the knee pain which required surgery. As a savvy consumer of statistics, what should you conclude?
Because this was only an observational study, the researchers should not make claims that the knee pain was caused by high heels.
Choose all the methods that apply to find the least-squares line.
Choose the line that makes the sum of squares of vertical distances as small as possible. Determine the vertical distances of each data point from a line. Find the sum of squares of the vertical distances.
When can we interchange the x and y variables in the least-squares regression line equation?
Never.
Data were collected on daily ice cream sales at the dairy on a university campus and daily reports of the number of students having flu-like symptoms at the university health center. Ice cream sales and number of students having flu-like symptoms were found to be highly negatively correlated. What does this tell us?
That there must be a lurking variable like temperature linking these two variables.
An investigation of the relationship between height of a child and age (in months) found r2 = 0.64. Knowing this, we can say _____________.
The age of a child explains 64% of the variation in height.
Complete the following statement about the intercept in a regression line.
The intercept is the value of predicted y when x is equal to zero.
Choose "User‑entered data" as the data set. Enter the given pairs of values, putting the 𝑥‑ and 𝑦‑values in columns A and B, respectively. (7,10),(27,35),(24,25),(8,12),(10,19),(15,22)(7,10),(27,35),(24,25),(8,12),(10,19),(15,22) Examine the scatterplot for the data. Do the two variables appear to be strongly correlated? Does there appear to be any outliers?
Yes; There does not appear to be any outliers in the data.
Create a scatterplot with at least 88 points where the correlation is between 0.50.5 and 0.70.7. Now add another data point, in the upper-left corner of the scatterplot. This causes the correlation coefficient to _______________ . Then click and drag this point down to the lower-left corner of the scatterplot. As you move the point down, the correlation coefficient ___________________ .
become smaller; becomes larger
Which of the following is a source of error NOT eliminated when using big data to make predictions?
bias
An observational study_____.
can never establish cause and effect
Numerous studies have found a strong negative association between time spent watching television (x) and grades in school (y). In order to prove that more TV time causes bad grades we would need to do a(n) ________________. (Your answer should be one word.)
experiment
Researchers interviewed a group of women with knee pain awaiting knee replacement surgery. They also interviewed a group of women from the same geographical area with no knee pain. These researchers reported that wearing high-heeled shoes caused the knee pain which required surgery. The women's weight might also be a contributing factor to knee pain. Because we have no clear information on weights of these women, this would be a _________ variable.
lurking
Least-squares regression makes the _______ differences between the points and the line as small as possible.
vertical
George needs money to buy a motor scooter. He borrows $1000 from his favorite aunt who has agreed not to charge him interest. He agrees to pay $50 per month. What is the regression line for predicting the amount of money George owes (y) based on month (x)? Assume that the regression line is no longer valid after the loan is paid off.
y=1000−50x
George needs money to buy a motor scooter. He borrows $1000 from his favorite aunt who has agreed not to charge him interest. He agrees to pay $50 per month. In a regression model to represent his debt, the y-intercept will be _________.
$1000
Carlos has been saving $8 each week in a box under his bed. The equation that predicts y (how much money he has at week x) is y=20+8x. The value of r2 for this relationship is ______.
100%
A petabyte, used in massive company databases to search for information to make predictions, contains ________ bytes of data.
10^15
Researchers interviewed a group of women with knee pain awaiting knee replacement surgery. They also interviewed a group of women from the same geographical area with no knee pain. These researchers reported that wearing high-heeled shoes caused the knee pain which required surgery. Which of the following is true in regards to a potential lurking variable?
A woman's weight could be a reasonable cause to explain their knee pain rather than high-heeled shoes.
Numerous studies have found a strong negative association between time spent watching television (x) and grades in school (y). Proving that more TV time causes bad grades is difficult because ______.
All options are correct.
The general form for a linear equation is given as: y = a + bx This regression model is appropriate in which situation?
For only linear relationships.
Use the Statistical Applet: Correlation and Regression to answer the question. Create a scatterplot with at least 88 points where the correlation is between 0.50.5 and 0.70.7. Adding a data point in the upper-left corner of the scatterplot causes the correlation coefficient to become smaller. Moving the additional data point to the lower-left corner of the scatterplot causes the correlation coefficient to become larger. Why does this occur? Select the correct explanation.
Since the least-squares regression line in the original scatterplot has a positive slope, a new data point in the upper-left corner of the scatterplot represents an outlier that pulls the regression line up, reducing the correlation coefficient. As the point is moved to the lower-left corner, it becomes less of an outlier and the correlation coefficient becomes larger.
The general form for a linear equation is given as: y = a + bx What does a in this equation tell us?
The predicted y for x = 0.
The following graph shows the linear relationship between diamond size and price for diamonds sized 0.35 carats or less. These diamonds were all of the same cut and clarity.
The setting of the diamond is a lurking variable in this relationship.
What does 0.59 represent in the following least-squares line? Petal length = 6.48+0.59 stigma height
The slope of the line
Weather forecasters tell people where a hurricane might strike so that they can evacuate for their safety. But sometimes people evacuate and the hurricane misses the area, making them angry at the forecasters and civil defense authorities who ordered the evacuation. Please select the correct answer based on the given information.
These errors in the forecast could be due to extrapolation
The response variable, y, and the explanatory variable, x,:
cannot be interchanged in the least-squares regression line equation.
If we simply want to know about association between two quantitative variables, we would use _______.
correlation
To establish clearly that an explanatory variable causes changes in a response variable, we need to perform a(n) ___________. (Your answer should be one word.)
experiment
In examining a relationship between two variables, the variable used to (hopefully) predict the second is called the ___________ variable.
explanatory
A simple random sample of n = 9 students in a statistics course was taken. For each student, their score on an anxiety test (x) and their first exam score (y) were recorded and are summarized in the following scatterplot. One student scored 44 on the anxiety test and wanted to know her predicted exam score. Using this model to make a prediction for this student would be _________.
extrapolation
The relationship between the number of televisions per capita (x) and average life expectancy of people (y) in various countries around the world has a strong positive correlation. Because of this, we should ________.
look for other potential reasons to explain the relationship.
Massive databases containing _____ of data (or 1015 bytes) are used by companies to attempt to find patterns and make predictions.
petabytes
The general form for a linear equation is given as: y = a + bx The quantity telling us how much y changes for a one-unit increase in x is called the ______.
slope
A quantity that measures the amount of variation in y explained by a regression model is the ____________ of the correlation coefficient.
square; r2 measures the amount of variation in y that is explained by the regression model.