Chapter 14 Regression Analysis

How many explanatory variables does a simple linear regression model have?

1

In a study, SST=1,000, SSE=200. Find the coefficient of determination.

Coefficient of determination= 1- SSE/SST 0.80

Error sum of squares (SSE)

In ANOVA, a measure of degree of variability that exists even if all population means are the same. In regression analysis, it measures the unexplained variation in the response variable

Simple linear regression model

In regression analysis, one explanatory variable is used to explain the variability in the response variable

In regression analysis, the response variable is also called the ___.

dependent variable

The residual e represents ...

the difference between an observed & predicted value of the response variable at a given value of the explanatory variable

Consider the simple linear regression model: y= β0 +β1x +ℇ Which symbol represents the intercept? - β1 - y - ℇ - β0 - x

β0

Residual e

In regression analysis, the difference between the observed value and the predicted value of the response variable, that is e= y- ŷ

What values can the coefficient of determination, R2, assume?

0 ≤ R2 ≤ 1

Which of the following are goodness-of-fit measure? - Coefficient of variation - Adjusted coefficient of determination - Standard error of the estimate - Coefficient of determination

- Adjusted coefficient of determination - Standard error of the estimate - Coefficient of determination

Explanatory variable

In regression analysis, the variance that influences the responses variable. They are also called the independent variables, predictor variables, control variable, or regression

In a simple linear regression model, if all of the data points fall on the sample regression line, then the standard error of the estimate is __.

0

In a simple linear regression model, if all of the data points fall on the sample regression line, then the coefficient of determination is ___.

1 (100% of the variation in y would be explained in that case)

If the sample regression equation is found to be ŷ= 20 + 10x, What is the predicted value of y when x = 3?

50

Adjusted R²

A modification coefficient of determination that imposes a penalty for using additional explanatory variables in the linear regression model

Ordinary least squares (method of least squares)

A regression technique for a straight line whereby the error (residual) sum of squares is minimized

Which of the following statements best defines a test statistic in a hypothesis test? - A mean upon which the decision in hypothesis testing is based - A variable upon which the decision in hypothesis testing is based - A mode upon which the decision in the hypothesis testing is based - A median upon which the decision in the hypothesis testing is based

A variable upon which the decision in hypothesis testing based

Which of the following identifies the range for a correlation coefficient? - Any value between -1 and 1, inclusive - Any value between 0 and 1, inclusive - Any value less than 1 - Any greater than 1

Any value between -1 and 1, inclusive

If two variables X1 and Y1 have a covariance of 25 and two other variables X2 and Y2 have a covariance of 65, what conclusion can we draw about the relationships?

Each set shows a positive linear relationship

Consider the following sample regression equation: ŷ=17+ 5x1+ 3x2. Interpret the value 5.

For a unit increase in x1 the average value of y increases by 5 units, holding x2 constant

Name the mathematical method that produces the "best-fitting trend line".

Ordinary least squares

What type of relationship exists between two variables if as one increases, the other increases?

Positive

coefficient of determination

The proportion of the sample variation in the response variable that is explained by sample regression equation

The multiple regression model used when?

The researcher believes that two or more explanatory variable influence the response variable

For which of the following situations is the multiple regression model appropriate? - The explanatory variable is influenced by two or more response variables - The explanatory variable is influenced by one response variable - The response variable is influenced by only one explanatory variable - The response variable is influenced by two or more explanatory variables

The response variable is influenced by two or more explanatory variables

In evaluating a regression model, why is a scatterplot a useful tool?

The scatterplot can be used to assess the linearity of the relationship.

Standard error of the estimate

The standard deviation of the residual; used as a goodness-of-fit measure for regression analysis

When conducting a hypothesis test, we determine ...

Whether the sample data support the alternative hypothesis

When testing whether the correlation coefficient differs from 0, the value of the test statistic is t20= 2.60 with a corresponding p-value of 0.0171. At 5% significance level, can you conclude that the correlation coefficient differs from 0?

Yes, since the p-value is less than 0.05 (Since the p-value= 0.0171<0.05=a, we reject the null hypothesis that the correlation coefficient equals 0.

In a simple linear regression model, which of the coefficients in the estimated sample regression equation indicates the change in the predicted value of y when x increases by 1 unit?

b1

In practice, we use a stochastic model over a deterministic model because...

certain variables that impact the response variable are not included in the model.

One limitation of correlation analysis is that it ...

may not be reliable measure when outliers are present in one or both of the variables

The common approach to fitting a line to a sample data in a scatterplot is to ...

minimize the value of the sum of the squared residuals

If the value of the sample covariance between the two random variables X and Y equals 14.67, then we can conclude that X and Y have a (an) ___.

positive linear relationship

The standard error of the estimate is the standard deviation of the ____.

residuals

For which of the following situations is a simple linear regression model appropriate? - The response variable y is influenced by two or more explanatory variables - The explanatory variable x is influenced by one response variable - The explanatory variable x is influenced by two or more response variables - The response variable y is influenced by one explanatory variable

the response variable y is influenced by one explanatory variable

Consider the simple linear regression model: y=B0 + B1x+ E Which of the following symbol represents the response variable? - x - ℇ - β - y - β0

y

If the sample regression equation is found to be (^ over y)= 10-2x1+3x2 the predicted value of y when x1=4 and x2=1 is ____.

ŷ=10 - 2(4) + 3(1) =5