Question 1

In order to predict with 90% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 10 observations is taken. Which of the following t-table values listed below would be used?
A) 1.812
B) 1.860
C) 2.228
D) 2.306

Accepted Answer

The answer of In order to predict with 90% confidence...

Question 2

The confidence interval estimate of the expected value of y for a given value x, compared to the prediction interval of y for the same given value of x and confidence level, will be:
A) wider.
B) the same.
C) narrower.
D) impossible to know.

Accepted Answer

The confidence interval estimate of the expected value of y for a given x is narrower than the prediction interval for y at the same x and confidence level because the prediction interval also accounts for the variability (error) in individual y values around the regression line, not just the uncertainty in estimating the mean of y.

Question 3

In order to predict with 98% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 15 observations is taken. Which of the following t-table values listed below would be used?
A) 1.350
B) 1.771
C) 2.160
D) 2.650

Accepted Answer

To predict the expected value of y with 98% confidence, we need to find the t-value that corresponds to a 98% confidence level and n-2 degrees of freedom, where n is the sample size. Since the sample size is 15, we have 13 degrees of freedom (n-2=15-2=13). Consulting a t-table with 13 degrees of freedom and a 98% confidence level, we find that the closest t-value is 2.650, which corresponds to answer choice D. Therefore, answer choice D would be used to predict the expected value of y with 98% confidence in this simple linear regression problem.

Question 4

A straight line regression model with only one independent variable is called a(n) ____________________-order linear model.

Accepted Answer

The answer of A straight line regression model with only...

Question 5

For a regression analysis to be valid, the value of the error variable associated with any particular value of y is ____________________ of the value of the error variable associated with any other value of y.

Accepted Answer

The answer of For a regression analysis to be valid,...

Question 6

SSE stands for ____________________ of squares for ____________________.

Accepted Answer

The answer of SSE stands for ____________________ of squares for...

Question 7

You cannot interpret the ____________________ of the simple linear regression line unless the value of x = 0 lies within the range of where data was collected.

Accepted Answer

The answer of You cannot interpret the ____________________ of the...

Question 8

In order to estimate with 95% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 10 observations is taken. Which of the following t-table values listed below would be used?
A) 2.228
B) 2.306
C) 1.860
D) 1.812

Accepted Answer

We need to use a t-table value with 9 degrees of freedom for a sample of size 10, and a 95% confidence level. The closest value in the t-table to 2.306 is 2.262, which is the value we would use. Therefore, the answer is B.

Question 9

The method statisticians use to produce a straight line that minimizes the SSE is called the ____________________ method.

Accepted Answer

The answer of The method statisticians use to produce a...

Question 10

In regression analysis, you predict the value of one variable on the basis of one or more other related variables. The variable being predicted is called the ____________________ variable, and the related variables used to make the prediction are called ____________________ variables.

Accepted Answer

The answer of In regression analysis, you predict the value...

Question 11

If the standard error of estimate is ____________________, this implies that the model's fit is poor.

Accepted Answer

The answer of If the standard error of estimate is...

Question 12

The width of the confidence interval estimate for the predicted value of y depends on
A) the standard error of the estimate
B) the value of x for which the prediction is being made
C) the sample size
D) All of these choices are true.

Accepted Answer

The width of the confidence interval estimate for the predicted value of y is influenced by all of the mentioned factors. The standard error of the estimate represents the spread of the residuals around the regression line and affects the precision of the estimate. The value of x for which the prediction is being made influences the slope of the regression line and the strength of the relationship between x and y, which in turn affects the precision of the estimate. Finally, the sample size affects the precision of the estimate by reducing the standard error of the estimate and increasing the degrees of freedom. Therefore, all of these factors affect the width of the confidence interval estimate for the predicted value of y.

Question 13

For a regression analysis to be valid, the error variable must have a(n) ____________________ distribution.

Accepted Answer

The answer of For a regression analysis to be valid,...

Question 14

The deviations between the actual data points and the fitted values from the model are called ____________________.

Accepted Answer

The answer of The deviations between the actual data points...

Question 15

For a regression analysis to be valid, the error variable must have a mean of ____________________.

Accepted Answer

The answer of For a regression analysis to be valid,...

Question 16

In a simple linear regression model b₁ is the ____________________ of the straight line.

Accepted Answer

The answer of In a simple linear regression model b₁...

Question 17

In a simple linear regression model b₀ is the ____________________ of the straight line.

Accepted Answer

The answer of In a simple linear regression model b₀...

Question 18

Suppose the slope of a simple linear regression line between hours studying and exam score is 5. That means as ____________________ increases by one, ____________________ increases by 5.

Accepted Answer

The answer of Suppose the slope of a simple linear...

Question 19

The objective of a regression model is to analyze the relationship between two variables, x and y, both of which must be based on ____________________ data.

Accepted Answer

The answer of The objective of a regression model is...

Question 20

In order to predict with 80% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 15 observations is taken. Which of the following t-table values listed below would be used?
A) 1.350
B) 1.771
C) 2.160
D) 2.650

Accepted Answer

The answer of In order to predict with 80% confidence...

Quiz 16: Simple Linear Regression and Correlation

In order to predict with 90% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 10 observations is taken. Which of the following t-table values listed below would be used?

The confidence interval estimate of the expected value of y for a given value x, compared to the prediction interval of y for the same given value of x and confidence level, will be:

In order to predict with 98% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 15 observations is taken. Which of the following t-table values listed below would be used?

A straight line regression model with only one independent variable is called a(n) ____________________-order linear model.

For a regression analysis to be valid, the value of the error variable associated with any particular value of y is ____________________ of the value of the error variable associated with any other value of y.

SSE stands for of squares for .

You cannot interpret the ____________________ of the simple linear regression line unless the value of x = 0 lies within the range of where data was collected.

In order to estimate with 95% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 10 observations is taken. Which of the following t-table values listed below would be used?

The method statisticians use to produce a straight line that minimizes the SSE is called the ____________________ method.

In regression analysis, you predict the value of one variable on the basis of one or more other related variables. The variable being predicted is called the variable, and the related variables used to make the prediction are called variables.

If the standard error of estimate is ____________________, this implies that the model's fit is poor.

The width of the confidence interval estimate for the predicted value of y depends on

For a regression analysis to be valid, the error variable must have a(n) ____________________ distribution.

The deviations between the actual data points and the fitted values from the model are called ____________________.

For a regression analysis to be valid, the error variable must have a mean of ____________________.

In a simple linear regression model b₁ is the ____________________ of the straight line.

In a simple linear regression model b₀ is the ____________________ of the straight line.

Suppose the slope of a simple linear regression line between hours studying and exam score is 5. That means as increases by one, increases by 5.

The objective of a regression model is to analyze the relationship between two variables, x and y, both of which must be based on ____________________ data.

In order to predict with 80% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 15 observations is taken. Which of the following t-table values listed below would be used?

Quiz 16: Simple Linear Regression and Correlation

In order to predict with 90% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 10 observations is taken. Which of the following t-table values listed below would be used?

The confidence interval estimate of the expected value of y for a given value x, compared to the prediction interval of y for the same given value of x and confidence level, will be:

In order to predict with 98% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 15 observations is taken. Which of the following t-table values listed below would be used?

A straight line regression model with only one independent variable is called a(n) ____________________-order linear model.

For a regression analysis to be valid, the value of the error variable associated with any particular value of y is ____________________ of the value of the error variable associated with any other value of y.

SSE stands for ____________________ of squares for ____________________.

You cannot interpret the ____________________ of the simple linear regression line unless the value of x = 0 lies within the range of where data was collected.

In order to estimate with 95% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 10 observations is taken. Which of the following t-table values listed below would be used?

The method statisticians use to produce a straight line that minimizes the SSE is called the ____________________ method.

In regression analysis, you predict the value of one variable on the basis of one or more other related variables. The variable being predicted is called the ____________________ variable, and the related variables used to make the prediction are called ____________________ variables.

If the standard error of estimate is ____________________, this implies that the model's fit is poor.

The width of the confidence interval estimate for the predicted value of y depends on

For a regression analysis to be valid, the error variable must have a(n) ____________________ distribution.

The deviations between the actual data points and the fitted values from the model are called ____________________.

For a regression analysis to be valid, the error variable must have a mean of ____________________.

In a simple linear regression model b1 is the ____________________ of the straight line.

In a simple linear regression model b0 is the ____________________ of the straight line.

Suppose the slope of a simple linear regression line between hours studying and exam score is 5. That means as ____________________ increases by one, ____________________ increases by 5.

The objective of a regression model is to analyze the relationship between two variables, x and y, both of which must be based on ____________________ data.

In order to predict with 80% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 15 observations is taken. Which of the following t-table values listed below would be used?

SSE stands for of squares for .

In regression analysis, you predict the value of one variable on the basis of one or more other related variables. The variable being predicted is called the variable, and the related variables used to make the prediction are called variables.

In a simple linear regression model b₁ is the ____________________ of the straight line.

In a simple linear regression model b₀ is the ____________________ of the straight line.

Suppose the slope of a simple linear regression line between hours studying and exam score is 5. That means as increases by one, increases by 5.