28. Simple Linear Regression

No apparent relationship

A situation where the points are randomly scattered throughout the graph, R-Squared would be zero. Most relationships are between these extremes,

What can be said about an R-Squared if 1.25

An R-Squared if 1.25 is not possible

Independent Variables

Are those variables that hopefully do the explaining. For example, income is the independent variable and sales is the dependent variable. Dependent variables depend upon the independent variable (sales depends upon income).

The ______ variable is the variable whose behavior we would like to explain.

Dependent

If the p-value associated with a regression analysis is greater than the critical p-value of 0.05 the regression line can be considered significant

False

In a scatter plot the independent variable is plotted on the Y axis

False

The number of packing errors has been found to be related to the number of hours of training taken by those working in the packing and shipping department. The number of hours of training represents the dependent variable

False

The null hypothesis in a linear regression states that a relationship exists between the dependent and independent variables

False - it should state that a linear relationship does not exist. Remember, the alternative hypothesis represents what it is you are trying to prove. In this situation you are trying to prove that a relationship does exist.

The coefficient of the independent variable identifies where the Regression line crosses

False -the letter a represents the place where the regression line crosses the Y axis. It is called the intercept.

In linear regression, the relationship between the dependent and independent variable can be expressed as a straight or curved line.

False it is a straight line, hence the name "Linear" regression.

When there is no apparent relationship between the independent and dependent variables in a simple Linear Regression model the R-Squared Value would be greater than 1.0

False it would be zero

The R-Squared is 0.46. This implies that 54 percent of the variation associated with the dependent variable has been explained.

False- 0.46 has been explained

Regression Analysis

Helps us to gain insight into relationships between two or more variables. For example, the relationship between sales and personal income. Are higher income associated with higher sales, but more important, what is the magnitude of this relationship.

Perfect Relationship

If all points on a line chart fall on a straight line, a perfect relationship would exist; we would say that the degree of the relationship is very strong. In statistics this is represented by a R-squared of 1.0

Dependent Variable

Is the variable whose behavior we would like to explain or predict.

Simple Linear Regression Model

It is simple because it involves only two variables I.e, income & sales. It is linear because it assumes that the relationship between these two variables can be expressed as a straight line.

The regression line determined by regression analysis is called the ______.

Line of best fit

A perfect relationship between a dependent and independent variable in a simple Linear Regression model would lead to a R-Squared of 1.0

True

A regression analysis has found that job satisfaction depends upon how long an employee has worked for a company. Job satisfaction is the dependent variable.

True

A two-tailed p-value is usually conducted to determine if the coefficient of the independent variable is significant

True

Data has been collected for two variables and a regression line computed. The regression line must be considered a sample result from many possible regression lines:

True

One of the distinguishing features of Simple Linear Regression is that there is only one independent variable.

True

The intercept is the point where the regression line crosses the Y axis.

True

The p-value associated with the independent variable is 0.001. The coefficient is therefore significant.

True

Regression analysis helps us gain insight into relationships between ____ or more variables.

Two or more

What is the mathematical representation of the regression line when there is one dependent variable and one independent variable

Y=a+bX