Question 1

The least squares technique minimizes the sum of the squares of the vertical distances between the actual Y values and the predicted values of Y.

Accepted Answer

This is the definition of the least squares technique. It minimizes the sum of the squares of the vertical distances between the actual Y values and the predicted values of Y.

Question 2

A regression equation is a mathematical equation that defines the relationship between two variables.

Accepted Answer

A regression equation is a mathematical equation that models the relationship between a dependent variable and one or more independent variables.

Question 3

Pearson's coefficient of correlation can be used if the data is nominally scaled.

Accepted Answer

Pearson's coefficient of correlation can only be used if the data is interval or ratio scaled, not nominally scaled.

Question 4

The coefficient of determination is equal to or greater than zero.

Accepted Answer

The coefficient of determination (r squared) is always between 0 and 1, inclusive. Therefore, it is equal to or greater than zero.

Question 5

One assumption underlying linear regression is that the Y values are statistically dependent.This means that in selecting a sample,the Y values chosen,for a particular X value,depend on the Y values for any other X value.

Accepted Answer

The answer of One assumption underlying linear regression is that...

Question 6

A t test is used to test the significance of the coefficient of correlation.

Accepted Answer

The answer of A t test is used to test...

Question 7

To test the significance of Pearson's r,we use the standard normal z distribution.

Accepted Answer

The significance of Pearson's r is typically tested using the t-distribution, not the standard normal z distribution.

Question 8

When testing the strength of the relationship between two variables,the alternate hypothesis is:

Accepted Answer

The alternate hypothesis is a statement that indicates the presence of a relationship between two variables. Therefore, when testing the strength of the relationship between two variables, the alternate hypothesis is true.

Question 9

In regression analysis,we expect prediction error or (  - Y)does not equal zero.

Accepted Answer

In regression analysis, we do not expect the prediction error to be exactly zero. This is because there is always some degree of variability or randomness in the relationship between the predictor variables and the response variable. Therefore, we expect the prediction error to be non-zero and strive to minimize it through various techniques such as least squares regression.

Question 10

The regression equation is used to estimate a value of the dependent variable Y based on a selected value of the independent variable X.

Accepted Answer

This is a true statement. The regression equation uses a mathematical formula to predict or estimate the value of the dependent variable Y based on the independent variable X.

Question 11

In order to visualize the regression equation line,we can draw a scatter diagram.

Accepted Answer

A scatter diagram can help visualize the relationship between variables and plot the regression line for a linear regression equation.

Question 12

The technique used to measure the strength of the relationship between two variables using the coefficient of correlation and the coefficient of determination is called regression analysis.

Accepted Answer

Regression analysis involves estimating the relationships among variables, while the coefficient of correlation and the coefficient of determination are specific measures used to assess the strength and proportion of variance explained in these relationships, respectively.

Question 13

The standard error of estimate is used to construct confidence intervals when the sample size is large and the scatter about the regression line is somewhat normally distributed.

Accepted Answer

This is correct. The standard error of estimate is a measure of the variability of actual y values around the predicted y values. When the scatter of the residuals is somewhat normally distributed, the standard error of estimate can be used to construct confidence intervals for the population values. However, when sample size is small, the distribution of the standard error of estimate will be skewed, and it will be less reliable for constructing confidence intervals.

Question 14

If the coefficient of determination is expressed as a percent,its value is between 0% and 100%.

Accepted Answer

The coefficient of determination, also known as R squared, is a number between 0 and 1. When expressed as a percentage, it is between 0% and 100%.

Question 15

The least squares principle is used to determine the best-fitting line.

Accepted Answer

The least squares principle is a method used to find the line that best fits a set of data. It minimizes the sum of the squared distances between each data point and the line. Therefore, option A is correct.

Question 16

A confidence interval can be determined for the mean value of Y for a given value of X.

Accepted Answer

A confidence interval can be calculated for the mean value of Y for a given value of X using regression analysis.

Question 17

Trying to predict weekly sales with a standard error of estimate of $1,955,we would conclude that 68 percent of the predictions would not be off more than $1,955,95 percent would not be off by more $3,910,and 99.7 percent would not be off by more than $5,865.

Accepted Answer

The standard error of estimate follows a normal distribution, where approximately 68% of values lie within ±1 standard deviation, 95% within ±2, and 99.7% within ±3. The given values align with these percentages.

Question 18

The values of a and b in the regression equation are called the regression coefficients.

Accepted Answer

The regression coefficients are the variables that represent the slope and intercept of the regression line, also known as a and b in the regression equation. Therefore, the statement is true.

Question 19

One assumption underlying linear regression is that for each value of X there is a group of Y values that is normally distributed.

Accepted Answer

This assumption is also known as the assumption of normality of residuals, which assumes that the residuals (the difference between observed Y and predicted Y) at each X value follows a normal distribution.

Question 20

When testing the strength of the relationship between two variables,the null hypothesis is:

Accepted Answer

The null hypothesis in testing the strength of the relationship between two variables is that there is no significant relationship between the two variables.

Quiz 13: Linear Regression and Correlation