Ch. 14

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 regression, if Multiple R equals 0.80, then R2 equals

0.64. 0.80x0.80 = 0.64

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.

Given the sample regression equation yhat=15+3x, which of the following is the value of the residual at the point (1,19).

1. yhat=15+3(1)=18; y-yhat=19-18=1.

Given the sample regression equation yhat=15+3x, which of the following is the value of the residual at the point (0,25).

10. yhat=15+3(0)=15; y-yhat=25-15=10.

If the sample regression equation is found to be yhat=30+5x, what is the estimate for the slope coefficient B1?

5.

If the sample regression equation is found to be yhat=20+10x, what is the Predicted value of y when x=3?

50.

What values will be considered Outliers in the following data set of ages of ten college students? 18,18,20,19,22,21,25,23,28,68.

68.

Which of the following is a goodness-of-fit measure?

Coefficient and determination.

Which of the following is another name for R2?

Coefficient of determination.

What is the difference between correlation and causation?

Correlation means that two variables are related, but causation means one causes the other to happen.

Consider the following sample regression equation: yhat=17-3x1+3x2. What will be the average change in the estimated value of y, given a unit change in x1(holding x2 constant)?

Decreased by 3 units.

Consider the simple linear regression model: y=B0+B1x+E. What is the notation for the random error term?

E.

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.

When testing whether the correlation coefficient differs from zero, the value of the test statistic is t20=1.95 with a corresponding p-value of 0.0653. At the 5% significance level, can you conclude that the correlation coefficient differs from zero?

No, since the p-value exceeds 0.05.

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

One.

If one variable decreases as the other variable decreases, the two variables have that type of relationship?

Positive

If the sample regression equation is yhat=15+5x, which of the following is the correct interpretation of 15?

The line crosses the y-axis at y=15.

Unlike R2, adjusted R2 accounts for

The sample size and the number of response variables.

Which of the following is a possible advantage of using multiple tools to judge the validity of a regression model?

To avoid the risk of using the wrong model.

When is the multiple regression model used?

When the researcher believes that two or more explanatory variables influence the response variable.

When do we use the alternative hypothesis: the population correlation coefficient is lass than zero?

When we test if two variables are negatively linearly related.

The estimated linear regression equation is yhat=-15+3x. Interpret the intercept.

When x=0, the predicted value of y is -15.

When conducting a hypothesis test, we determine

Whether the sample data support the alternative hypothesis.

The goodness-of-fit measure that quantifies the proportion of the variation in the response variable that is explained by the sample regression equation is the

coefficient of determination.

In regression analysis, the response variable is also called the

dependent variable.

When the response variable is uniquely determined by the explanatory variable, the relationship is

deterministic.

Unlike R2, adjusted R2 can be used to compare regression models with

different numbers of explanatory variables.

In hypothesis tests about the population correlation coefficient, the alternative hypothesis of not equal to zero is used when testing whether two variables are

linearly related.

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

minimize the value of the sum of the squared residuals.

In regression model, the residual e is calculated as

y-yhat.

If the sample regression equation is to be yhat = 10+2x1-3x2, what is predicted valueof y when x1 = 4 and x2 = 1?

yhat = 10 + 2(4) - 3(1) = 15

If the sample regression equation is found to be yhat+10-2x1-3x2, what is the predicted value of y when x1=4 and x2=1?

-1.

Which of the following is NOT true of the standard error of the estimate?

It can take on negative values.

If the correlation between the response variable and the explanatory variable is sufficiently low, then adjusted R2

May be negative.

The residual e represents

The difference between an observed and predicted value of the response variable at a given value of the explanatory variable.

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

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

The R2 of a multiple regression of y as a function of x measures the

percentage variability of y that is explained by the variability of x.

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

residuals.

One limitation of correlation analysis is that it

does not imply causation.

Consider the simple linear regression model: y=B0 + B1x +E. What is the notation for the intercept?

B0.

Consider the simple linear regression model: y=B0+B1x+E. What is the notation for the slope coefficient?

B1.

The standard error of the estimate can assume which of the following values?

Between zero and infinity.

The coefficient of determination can assume which of the following values?

Between zero and one.

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

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

In regression analysis, the explanatory variable is also called the

Independent variable.

In an attempt to predict a single response variable y, three models are estimated. The standard error of the estimate for Model 1 equals 10, for Model 2 equals 100, and for Model 3 equals 1000. According to the standard error of the estimate, which model provides the best fit?

Model 1

Suppose that the slope parameter in a simple linear regression model is B1=3.52. What does this possibly suggest about the nature of the relationship between x and y?

Positive linear relationship.

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

Positive.

For which of the following situations is a simple linear regression model appropriate?

The response variable y is influenced by one explanatory variable.

In a study, the estimated linear regression equation is given as yhat=20-3x. Interpret the estimated slope coefficient.

The slope is negative, indicating a negative linear relationship.

Which of the following statements is true about the test of Ho : Pxy = 0?

The test statistic is assumed to follow the tdf distribution with n-2 degrees of freedom.

SST respresents

The total variation in y.

The graph used to show the relationship between two variables is the

scatterplot.

If rxy = 0.83, then we conclude that X and Y have relatively

strong, positive linear relationship.