Question

In: Statistics and Probability

In simple linear regression, r 2 is the _____. a. coefficient of determination b. coefficient of...

In simple linear regression, r 2 is the _____.

a.

coefficient of determination

b.

coefficient of correlation

c.

estimated regression equation

d.

sum of the squared residuals

QUESTION 3

A least squares regression line ______.

a.

may be used to predict a value of y if the corresponding x value is given

b.

implies a cause-effect relationship between x and y

c.

can only be determined if a good linear relationship exists between x and y

d.

All of the answers are correct.

QUESTION 4

Regression analysis was applied between sales (in $1000s) and advertising (in $100s), and the following regression function was obtained.

= 80 + 6.2x

Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is _____.

a.

$700,000

b.

$700

c.

$142,000

d.

$62,080

QUESTION 5

In a regression analysis, the variable that is used to predict the dependent variable ______.

a.

is the dependent variable

b.

must have the same units as the variable doing the predicting

c.

usually is denoted by x

d.

is the independent variable

QUESTION 6

The equation that describes how the dependent variable ( y) is related to the independent variable ( x) is called _____.

a.

the correlation model

b.

the regression model

c.

correlation analysis

d.

None of the answers is correct.

QUESTION 7

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is called _____.

a.

a prediction interval

b.

the standard error

c.

a residual

d.

the variance

QUESTION 8

Regression analysis is a statistical procedure for developing a mathematical equation that describes how _____.

a.

one independent and one or more dependent variables are related

b.

several independent and several dependent variables are related

c.

one dependent and one or more independent variables are related

d.

None of the answers is correct

QUESTION 9

A procedure used for finding the equation of a straight line that provides the best approximation for the relationship between the independent and dependent variables is ______.

a.

the most squares method

b.

the least squares method

c.

correlation analysis

d.

the mean squares method

Solutions

Expert Solution

2)

In simple linear regression, r 2 is the

a.

coefficient of determination

3)

A least squares regression line _

a.

may be used to predict a value of y if the corresponding x value is given

4)

The equation of regression line is,

where

x = advertising

Given

X = $10,000,

The point estimate for sales (in dollars) is $62,080.

The correct option is

d.$62,080

5)

In a regression analysis, the variable that is used to predict the dependent variable

d.

is the independent variable

6)

The equation that describes how the dependent variable ( y) is related to the independent variable ( x) is called

b.

the regression model

7)

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is called

c.

a residual

8)

Regression analysis is a statistical procedure for developing a mathematical equation that describes how

c.

one dependent and one or more independent variables are related

9)

A procedure used for finding the equation of a straight line that provides the best approximation for the relationship between the independent and dependent variables is

b.

the least squares method


Related Solutions

Compare the coefficients of determination (r-squared values) from the three linear regressions: simple linear regression from...
Compare the coefficients of determination (r-squared values) from the three linear regressions: simple linear regression from Module 3 Case, multivariate regression from Module 4 Case, and the second multivariate regression with the logged values from Module 4 Case. Which model had the “best fit”? Calculate the residual for the first observation from the simple linear regression model. Recall, the Residual = Observed value - Predicted value or e = y – ŷ. What happens to the overall distance between the...
What is a simple linear regression model?   What does the value of the linear correlation coefficient...
What is a simple linear regression model?   What does the value of the linear correlation coefficient tell us? Please type the answer as I have diffculties understanding handwritten answers. Thanks.
You are developing a simple linear regression analysis model. The simple correlation coefficient between y and...
You are developing a simple linear regression analysis model. The simple correlation coefficient between y and x is -0.72. What do you know must be true about b1. The least squares estimator of B1? Why? In a multiple linear regression analysis with k = 3. From the t test associated with B1, you conclude that B1 = 0. When you do the f test will you reject or fail to reject the null hypothesis? Why? In a simple bilinear regression...
Another coefficient mentioned in this week's readings is the coefficient of determination, r^2. What information do...
Another coefficient mentioned in this week's readings is the coefficient of determination, r^2. What information do we obtain from this coefficient?
Find the equation of the least-squares regression line ŷ and the linear correlation coefficient r for...
Find the equation of the least-squares regression line ŷ and the linear correlation coefficient r for the given data. Round the constants, a, b, and r, to the nearest hundredth. {(0, 10.8), (3, 11.3), (5, 11.2), (−4, 10.7), (1, 9.3)}
Suppose you estimate a simple linear regression model and obtain a t-value for the slope coefficient...
Suppose you estimate a simple linear regression model and obtain a t-value for the slope coefficient of -3.1. Based on this, explain which of the following statements are correct or wrong: a) A 95% confidence interval for the true slope would exclude 0. b) It is possible that the point estimate for the slope is b_1=4. c) At the 10% level of significance you fail to reject the null hypothesis that the true slope is equal to 0. d) The...
Consider the simple linear regression mode
Consider the simple linear regression modelYi = β0 + β1xi + εi, where the errors εi are identically and independently distributed as N (0, σ2).(a) If the predictors satisfy x ̄ = 0, show that the least squares estimates βˆ0 and βˆ1 are independently distributed.(b) Let r be the sample correlation coefficient between the predictor and response. Under what conditions will we have βˆ1 = r?(c) Suppose that βˆ1 = r, as in part b), but make no assumptions on...
Discuss the application of simple linear regression
Discuss the application of simple linear regression
Simple Linear Regression: Suppose a simple linear regression analysis provides the following results: b0 = 6.000,    b1...
Simple Linear Regression: Suppose a simple linear regression analysis provides the following results: b0 = 6.000,    b1 = 3.000,    sb0 = 0.750, sb1 = 0.500,  se = 1.364 and n = 24. Use this information to answer the following questions. (a) State the model equation. ŷ = β0 + β1x ŷ = β0 + β1x + β2sb1    ŷ = β0 + β1x1 + β2x2 ŷ = β0 + β1sb1 ŷ = β0 + β1sb1 x̂ = β0 + β1sb1 x̂ = β0 +...
1. What is the difference between Pearson’s correlation coefficient, r, and the coefficient of determination, r2?...
1. What is the difference between Pearson’s correlation coefficient, r, and the coefficient of determination, r2? What does each statistic tell us about the relationship between two variables? What do these statistics NOT tell us about the relationship between two variables?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT