Question 1

Which of the following is the appropriate null hypothesis to test whether a population correlation is 0?

Accepted Answer

The answer of Which of the following is the appropriate...

Question 2

The value of the sum of squares for regression can never be larger than 100.

Accepted Answer

The value of the sum of squares for regression can be any large non-negative number, so it can be larger than 100.

Question 3

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

Accepted Answer

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

Question 4

Which of the following is an indication of no linear relationship between two variables x and y?

Accepted Answer

A coefficient of correlation of 0 indicates no linear relationship between two variables. A coefficient of correlation of 1 indicates a perfect positive linear relationship, while a coefficient of determination of -1 indicates a perfect negative linear relationship and a coefficient of determination of 1 indicates a perfect positive linear relationship.

Question 5

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

Accepted Answer

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

Question 6

In a simple linear regression , if the sum of squares for regression is 90, then the total sum of squares is at least 90.

Accepted Answer

The sum of squares for regression is always a part of the total sum of squares, so if the sum of squares for regression is 90, then the total sum of squares must be at least 90.

Question 7

A study of 20 students showed that the correlation between the time spent writing a test and the number of hours studied the night before the test was 0.35. Using a level of significance equal to 0.05, what does this imply?

Accepted Answer

A correlation coefficient of 0.35 indicates a weak positive correlation between the time spent writing the test and the number of hours studied the night before. With a level of significance of 0.05, we cannot reject the null hypothesis that the true correlation coefficient is 0. Therefore, we do not have enough evidence to conclude that there is a significant correlation between the two variables.

Question 8

In a simple linear regression , if the sum of squares for regression is 90, then the sum of squares for error is at most 90.

Accepted Answer

The sum of squares for error cannot be at most 90. It has to be greater than or equal to 0 since it represents the variation in the response variable that is not explained by the regression model. Therefore, the correct statement should be "the sum of squares for error is at least 90".

Question 9

A sample of 25 observations is selected, and the sample correlation coefficient between the variables x and y is r = 0.525. What is the test statistic value for testing  vs.

Accepted Answer

The answer of A sample of 25 observations is selected,...

Question 10

In a simple linear regression setting, the deterministic model equation determines an exact value of the dependent variable y when the value of the independent variable x is given, since all points must lie exactly on the line.

Accepted Answer

The answer of In a simple linear regression setting, the...

Question 11

In publishing the results of some research work, the following values of the correlation coefficient were listed. Which one is incorrect?

Accepted Answer

The correlation coefficient ranges between -1 and 1. A value of 1 indicates a perfect positive correlation while a value of -1 indicates a perfect negative correlation. A value of 0 indicates no correlation. However, the value of 1.05 is impossible as it exceeds the upper limit of 1.

Question 12

In order to predict with 99% confidence the expected value of y for a given value of x in a simple linear regression , a random sample of ten observations is taken. Which of the following t-table values would be used?

Accepted Answer

Since we are looking for a 99% confidence interval, we need to find the t-value that corresponds to a 0.005 (1-0.99/2) significance level and 9 degrees of freedom (n-2). Looking at the t-table, the closest value to 0.005 and 9 degrees of freedom is 3.355, which corresponds to Choice D. Therefore, we would use the t-value from Choice D to predict the expected value of y for a given value of x with 99% confidence.

Question 13

Given the least-squares regression line  = -4.63 + 1.38x, and a coefficient of determination of 0.9025, what is the correlation coefficient?

Accepted Answer

The correlation coefficient is the square root of the coefficient of determination, which is 0.9025. Therefore, the correlation coefficient is +/- 0.95. Since the regression line has a positive slope, the correlation coefficient is positive, so the answer is C.

Question 14

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

Accepted Answer

For a 98% confidence level with 14 degrees of freedom (n-1 = 15-1), the t-value is approximately 2.650.

Question 15

In a simple linear regression setting, the probabilistic model equation allows for some deviation of the points about the regression line, making it a more practical model.

Accepted Answer

The probabilistic model equation includes an error term to account for deviations of the data points from the regression line. This makes it a more realistic and practical model for real-world data.

Question 16

In a simple linear regression model, if the regression slope coefficient is negative, then the standard error of the estimate will be positive.

Accepted Answer

The standard error of the estimate measures the accuracy of predictions and is always positive, regardless of the sign of the slope coefficient.

Question 17

Which of the following statements is NOT a property of the residuals in simple linear regression model?

Accepted Answer

The statement that residuals have a median of 0 is not necessarily true in a simple linear regression model. The other statements (A, B, and D) are true properties of residuals in simple linear regression.

Question 18

In a simple linear regression , if the sum of squares for regression is 90, then the correlation coefficient is 0.9.

Accepted Answer

The given statement is false. The correlation coefficient cannot be determined solely from the sum of squares for regression. Additional information, such as the sum of squares for the total, is needed to calculate the correlation coefficient.

Question 19

The sum of squares for regression can never be larger than the sum of squares for error.

Accepted Answer

The sum of squares for regression represents the variability that the regression model is able to explain, while the sum of squares for error represents the variability that the regression model is unable to explain. Therefore, it is possible for the sum of squares for error to be larger than the sum of squares for regression, particularly if the model has poor fit.

Question 20

In a simple linear regression model, the regression slope coefficient will have the same sign as the correlation coefficient.

Accepted Answer

This is true because the correlation coefficient measures the direction and strength of the linear relationship between two variables, while the regression slope coefficient measures the change in the dependent variable for a unit change in the independent variable. If there is a positive correlation between the variables, then the regression slope coefficient will be positive as well. Similarly, if there is a negative correlation between the variables, then the regression slope coefficient will be negative.

Quiz 12: A: linear Regression and Correlation