If one variable decreases as the other variable decreases, the two variables have that type of relationship?
Positive
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.
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
Model 1
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 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.
When conducting a hypothesis test, we determine
Whether the sample data support the alternative hypothesis.
In evaluating a regression model, why is a scatterplot a useful tool?
The scatterplot can be used to assess the linearity of the relationship.
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.
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, if Multiple R equals 0.80, then R2 equals
0.64. 0.80x0.80 = 0.64
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.
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.
If the correlation between the response variable and the explanatory variable is sufficiently low, then adjusted R2
May be negative.
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.
What is the difference between correlation and causation?
Correlation means that two variables are related, but causation means one causes the other to happen.
Which of the following is a goodness-of-fit measure?
Coefficient and determination.
The standard error of the estimate is the standard deviation of the
residuals.
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.
Consider the simple linear regression model:
y=B0 + B1x +E.
What is the notation for the intercept?
B0.
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.
If rxy = 0.83, then we conclude that X and Y have relatively
strong, positive linear relationship.
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.
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.
What type of relationship exists between two variables if as one increases, the other increases?
Positive.
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+10-2x1-3x2, what is the predicted value of y when x1=4 and x2=1?
-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.
One limitation of correlation analysis is that it
does not imply causation.
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.
How many explanatory variables does a simple linear regression model have?
One.
The graph used to show the relationship between two variables is the
scatterplot.
Unlike R2, adjusted R2 can be used to compare regression models with
different numbers of explanatory variables.
The standard error of the estimate can assume which of the following values?
Between zero and infinity.
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.
Consider the simple linear regression model:
y=B0+B1x+E.
What is the notation for the slope coefficient?
B1.
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.
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.
The estimated linear regression equation is yhat=-15+3x. Interpret the intercept.
When x=0, the predicted value of y is -15.
If the sample regression equation is found to be yhat=20+10x, what is the Predicted value of y when x=3?
50.
The coefficient of determination can assume which of the following values?
Between zero and one.
Consider the simple linear regression model:
y=B0+B1x+E.
What is the notation for the random error term?
E.
Which of the following is NOT true of the standard error of the estimate?
It can take on negative values.
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.
Which of the following is another name for R2?
Coefficient of determination.
For which of the following situations is a simple linear regression model appropriate?
The response variable y is influenced by one explanatory variable.
When is the multiple regression model used?
When the researcher believes that two or more explanatory variables influence the response variable.
In regression analysis, the explanatory variable is also called the
Independent variable.
When the response variable is uniquely determined by the explanatory variable, the relationship is
deterministic.
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.
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 regression analysis, the response variable is also called the
dependent variable.
SST respresents
The total variation in y.
In regression model, the residual e is calculated as
y-yhat.