BUS255 - Chaper 14 LearnSmart
The sample regression equation is found to be ^y=10+2X1+3X2, what is the predicted value of y when X1=4 and X2=1?
21
Which of the following sample correlation coefficients shows the strongest linear association between X and Y? -0.85 -0.95 0.90 0.80
-0.95 (closest number to 1 or -1)
What values can the coefficient of determination, R^2, assume?
-1<=R^2<1
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 study, SST=1000, SSE=200. Find the coefficient of determination.
0.20 [1-(200/1000)=0.20]
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 ^y=15+3x, what is the value of the residual at the point (0,25)?
15
If the sample regression equation is found to be ^y=20+10x, what is the predicted value of y when x=3?
50
What is the range for a correlation coefficient?
Any value between -1 and 1, inclusive
Consider the simple linear regression model: y = B0 + B1x + E Which symbol represents the slope?
B1
Multiple R is which type of measurement?
Correlation coefficient
What is the difference between correlation and causation?
Correlation means that two variables are related, but causation means that one variable causes another to happen.
If two variables X1 and Y1 have a covariance of -100 and two other variables X2 and Y2 have a covariance of -1000, what conclusion can we draw about the relationships?
Each set shows a negative linear relationship.
If the sample regression equation is ^y=15+5x, what is the correct interpretation of 5?
For every unit increase in x, ^y increases, on average, by 5 units.
How many explanatory variables does a simple linear regression model have?
One
What is a possible disadvantage of removing outliers from a data set without investigation?
Outliers may contain important information about the relationship between the two variables.
What are used to judge the goodness-of-fit of a regression model?
Se, R^2, and adjusted R^2
When is the multiple regression model appropriate?
The response variable is influenced by two or more explanatory variables.
In a simple linear regression, an upward sloping trend line suggests:
a positive linear relationship between x and y.
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.
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 a regression model, the Multiple R is the:
correlation between the response variable and the predicted value
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
One limitation of correlation analysis is that it:
does not imply causation
In regression analysis, the explanatory variable is also called the:
independent variable
If the correlation between the response variable and the explanatory variables is sufficiently low, then the adjusted R^2:
may be negative
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.
If the value of the sample covariance between the two random variables X and Y equals -150, then we can conclude that X and Y have a(n):
negative linear relationship
Name the mathematical method that produces the "best-fitting trend line."
ordinary least squares
If the value of the sample covariance between two random variables X and Y equals 14.67, then we can conclude that X and Y have a(n):
positive linear relationship
The standard error of the estimate is the standard deviation of the:
residuals
The graph used to show the relationship between two variables is the:
scatterplot
The residual e represents:
the difference between an observed and predicted value of the response variable at a given value of the explanatory variable.
SST represents the:
total variation in y
We specify the alternative hypothesis as HA: p < 0, when we want to test if:
two variables are linearly related
What does the model y=B0+B1X+E tell us about the relationship between the variables x and y?
x and y are linearly related, but the relationship is inexact, or stochastic
