stats smartbook

Suppose that the slope in a simple linear regression model is β1 = -5.18. What does this suggest about the nature of the relationship between x and y?

Negative linear relationship

A(n) ______ is a value obtained from a sample that can be used to estimate a similar value from the larger population.

point estimate

The provided scatter plot depicts a ______ relationship between the x and y variables.

positive linear

A scatter plot is used to show the relationship between two _______.

quantitative variables

the __________ of measurements in a data set is calculated as the largest measurement minus the smallest measurement.

range

Suppose we are analyzing quantitative data that is fairly symmetrical around 50. If we add several data points in 100's, this will cause the distribution to become:

right skewed

A z score has units interpreted as _____________standard deviations from the mean.

standard deviations from the mean.

A sample ______ is a number calculated using the sample measurements that describes some aspect of the sample.

statistic

The sample standard deviation can be found by ________________ the sample variance.

taking the square root of

Which measure of central tendency is the same as the second quartile?

the median

Given the multiple regression analysis below, which of the following conclusions is true with regard to the overall F test at the 5% significance level?

At least one of the independent variables is significantly related to the dependent variable.

If a scatter plot of y versus x reveals a circular pattern of dots, it would be appropriate to describe the relationship using simple linear regression.

False

Regression can establish that one variable causes a change in another variable. Multiple choice question.

False

True or false: When predicting the value of y, given x, we use a value of 1 for the error term, ε.

False

Suppose the slope of a least squares line is 2.5. If x increases by 2, how do we anticipate y will change?

It should increase by approximately 5.

The provided scatter plot depicts the following relationship between the x and y variables.

More shelf space is related to more units sold.

The interquartile range is the difference between which two quartiles?

first and third

For populations that are positively or negatively skewed, the empirical rule tends to ______.

give unreliable descriptions of the distribution.

A sampling of prices for new and used houses found that the mean price for a new house is $120,000 and the standard deviation is $6100. It also found that the mean price for a used house is $50,000 and the standard deviation is $3150. Which of the following statements are true?

he coefficient of variation for new houses is 5.08% The coefficient of variation for used houses is 6.30%

Which of the following symbols is used to denote sample mean?

/x

Calculate the z score for the population value 7 where μ = 5 and σ = 2.

1

Calculate the z score for the population value 8.2 where μ = 5.46 and σ = 2.37 (rounded to two decimals).

1.16

Fund X has a mean return of 12.43 percent with a standard deviation of 14.5 percent. What is the coefficient of variation for Fund X?

116.65

If the least squares predication equation is found to be yˆŷ = 10 + 2x1 - 3x2, what is the predicted value of y when x1 = 4 and x2 = 1?

15

f the least squares predication equation is found to be yˆŷ = 10 + 2x1 - 3x2, what is the predicted value of y when x1 = 4 and x2 = 1?

15

Fund Y has a mean return of 22.1 percent with a standard deviation of 3.73 percent. What is the coefficient of variation for Fund Y?

16.88

Calculate the z score for the population value 6.5 where μ = 7.96 and σ = 0.42 (rounded to two decimals).

-3.48

If the least squares predication equation is found to be yˆŷ = 10 + 2x1 + 3x2, what is the predicted value of y when x1 = 1 and x2 = 4?

24

A simple linear regression model relating a student's university GPA, y, to his high school GPA, x, is given by yˆŷ = 1.097 + 0.675x Predict the university GPA of a student whose high school GPA is 3. You may assume that 3 is in the experimental region.

3.1

Using Chebyshev's Theorem, at least 93.75% of the population measurements lie within 93.75%Blank 1Blank 1 93.75% , Incorrect Unavailable standard deviations of the mean.

4

Given the following sample of ten numbers: 1, 4, 2, 5, 4, 4, 6, 4, 2, 1 Compute the range of the data set:

5 or five

am's exam score was good but 32% of students scored higher than Sam. That places Sam in the

68

A simple linear regression model relating a student's SAT score, y, to the number of hours she spent studying, x, is given by yˆŷ = 353.2 + 25.3x Predict the SAT score of a student who spends 15 hours studying. You may assume that 15 is in the experimental region.

732.7True or false: When predicting the value of y, given x, we use a value of 0 for the error term, ε. True false question.

The range of the data set 2, 5, 5, 7, and 10 is

8

Given the multiple regression analysis below, which of the following conclusions is true with regard to the overall F test at the 5% significance level? df SS MS F Significance F Regression 2 1,562 781 1.01 0.3821 Residual 20 15,395 770 Total 22 16,957

Neither of the independent variables is significantly related to the dependent variable.

The empirical rule tends to give unreliable estimations when for populations that are:

Positively skewed Negatively skewed

Suppose the histogram representing the salaries of all employees at a small company shows most salaries are bunched in the same region with just a few salaries substantially greater than the rest. How would you describe this distribution? Multiple choice question.

Right skewed distribution

True or false: The closer the multiple coefficient of determination is to 1, the better the model is at predicting y. True false question.

TRUE

True or false: The least squares prediction equation can be used to estimate the mean value of the dependent variable AND to predict an individual value of the dependent variable.

TRUE

Regression can ______

establish that two variables have a negative linear relationship. establish that two variables have a positive linear relationship.

The multiple coefficient of determination, R2, is calculated as ______ Multiple choice question.

explained variation / total variation

In the multiple regression model, y = β0 + β1x1 + β2x2 + ε, how is β1 interpreted?

The mean change in y associated with a one-unit increase in x1

In the multiple regression model, y = β0 + β1x1 + β2x2 + ε, how is β2 interpreted?

The mean change in y associated with a one-unit increase in x2

In the multiple regression model, y = β0 + β1x1 + β2x2 + ε, how is β0 interpreted?

The mean y value when x1 = 0 and x2 = 0

R2 is the multiple coefficient of determination. What is R? Multiple choice question.

The multiple correlation coefficient

The coefficient of variation for Fund Z is 77.34. What does this mean?

The standard deviation is 77.34 percent of the mean.

True or false: When predicting the value of y, given k independent variables, we use a value of 0 for the error term, ε. True false question.

True

True or false: When predicting the value of y, given x, we use a value of 0 for the error term, ε.

True

True or false: When predicting the value of y, given x, we use a value of 0 for the error term, ε. True false question.

True

Imagine a histogram of exam scores where most of the students scored 70% and up. Although a few scores were extremely low: 20% and below. These outliers would cause the histogram to be:

left skewed

Imagine a histogram of exam scores where most of the students scored 70% and up. Although a few scores were extremely low: 20% and below. These outliers would cause the histogram to be: Multiple choice question.

left skewed

For a set of measurements arranged in increasing order, the pth percentile is a value such that p percent of the measurements are _____ the value.

less than or equal to

For a set of measurements arranged in increasing order, the pth percentile is a value such that p percent of the measurements are _____ the value.

less than or equal two

The population ______ is the average of the population measurements.

mean

The least squares prediction equation can be used to estimate the mean value of the dependent variable and _____

to predict an individual value of the dependent variable.

True or false: The sample variance and sample standard deviation are point estimates for the population variance and population standard deviation.

true

rue or false: The sample variance and sample standard deviation are point estimates for the population variance and population standard deviation.

true

population _______________ is the average of the squared deviations from the population mean.

variance

When testing the significance of the independent variables, the provided regression analysis is obtained. Which variables can we conclude are significantly related to y at the 1% level of significance?

x2 x3

How do we predict the value of y, given x?

yˆŷ = b0 + b1x