busi stats ch 14
Unlike R2, adjusted R2 explicitly accounts for
the sample size and the number of explanatory variables
The standard error of the estimate measures ________.
the standard deviation of the random error
Which of the following is another name for R2?
Coefficient of determination
Which of the following are goodness-of-fit measures?
Coefficient of determination Adjusted coefficient of determination Standard error of the estimate
In a simple linear regression model, if the points on a scatter diagram lie on a straight line with a negative slope, which of the following is the coefficient of determination?
+1 From the given information Coefficient of determination is +1 Because slope is negative that means correlation coefficient is also negative. And all points lie on the straight line hence correlation is - 1 But coefficient of determination is 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
What values can the coefficient of determination, R2, assume?
0 ≤ R2 ≤ 1
What values can the standard error of the estimate, se, assume?
0 ≤ se < ∞
How many explanatory variables does a simple linear regression model have?
1
Formula for adjusted R2
1 - (1 - R2)(n−1/n−k−1)
Which of the following is the formula for the coefficient of determination.
1-SSE/SST SSR/SST
If the sample regression equation is found to be ŷŷ = 5 + 10x, what is the estimate for the intercept β0?
5
The standard error of the estimate measures ________.
the variability of the predicted y-values around the mean of the observed y-values
The standard error of the estimate can assume which of the following values?
Between zero and infinity
______ and _______ analysis are related in a sense that they both measure some form of association between variables.
Blank 1: Correlation Blank 2: Regression
The OLS method chooses the line whereby the _____ is minimized.
Blank 1: SSE
A common approach to fitting a line to the scatterplot is the method of
Blank 1: least Blank 2: squares
The difference between the observed and the predicted values of y represents the
Blank 1: residual or error
Regression presumes that one variable, called the _____variable, is influenced by other variables, called the _____ variables.
Blank 1: response or y Blank 2: explanatory or x
Our objective in adding another explanatory variable to a linear regression model is to increase the model's
Blank 1: usefulness
If the sample regression equation is ŷŷ = 15 + 5x, which of the following is the correct interpretation of 5?
For every unit increase in x, ŷŷ increases, on average, by 5 units.
Which of the following statements is TRUE about goodness-of-fit measures? Multiple Choice Goodness-of-fit measures are used to gauge the predictive power of a regression model. Goodness-of-fit measures are always improved by increasing the number of explanatory variables in a regression model. The higher the value of any goodness-of-fit measure, the better the model fit. Goodness-of-fit measures are used to assess how well the explanatory variables explain the variation in the response variable.
Goodness-of-fit measures are used to assess how well the explanatory variables explain the variation in the response variable.
Which of the following statements about regression analysis is FALSE? Multiple Choice It uses information on the explanatory variables to predict the value of the response variable. It can establish cause-and-effect relationships. It is related to correlation analysis. It can have multiple explanatory variables.
It can establish cause-and-effect relationships.
Which of the following is NOT true of the standard error of the estimate?
It can take on negative values.
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 Reason: The closer to zero, the better the fit.
If the sample regression equation is ŷ = 15 + 5x, which of the following is the correct interpretation of the estimated intercept?
The line crosses the y axis at y = 15.
Why is the stochastic model used in regression analysis in place of the deterministic model?
The relationship between the response and the explanatory variables is inexact, or imperfect.
The multiple regression model used when?
The researcher believes that two or more explanatory variables influence the response variable.
For which of the following situations is the multiple regression model appropriate?
The response variable is influenced by two or more explanatory variables.
For which of the following situations is a simple linear regression model appropriate?
The response variable y is influenced by one explanatory variable.
The use of the standard error of the estimate as a measure of a model's goodness-of-fit is best expressed by which of the following statements?
The smaller the value, the better the fit.
An estimated linear regression equation is ŷŷ = -15 + 3x. Interpret the intercept
When x = 0, the predicted value of y is -15. Reason: The regression equation does not provide observed values. Y is the predicted value.
Consider the sample regression equation yˆy^ = 12 + 3x1 − 5x2 + 7x3 − 2x4. When x1 increases by 1 unit and x2 increases by 2 units, while x3 and x4 remain unchanged, what change would you expect in the predicted y?
ans is c, as with one unit increase in x1 the predicted y increases by 3 with one unit inrease in x2 predicted y decrease by 5 so here ans is, 3-10= -7 Decrease by 7
Which of the following are the estimated model coefficients of the simple linear regression equation?
b0 and 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.
Consider the following sample regression equation yˆ y^ = 150 − 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). If the price of the good increases by $3, then we expect demand for Product A to ________.
decrease by 60,000
R2 never_____ as we add more explanatory variables to the model.
decreases
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
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.
The standard error of the estimate is the standard deviation of the
errors
What is the name of the variable that is used to predict another variable?
explanatory
Unlike the coefficient of determination, the sample correlation coefficient in a simple linear regression ________.
indicates whether the slope of the regression line is positive or negative
When two regression models applied on the same data set have the same response variable but a different number of explanatory variables, the model that would provide the better fit is the one with the
lower se and higher adjusted R2.
When two regression models applied on the same data set have the same response variable but a different number of explanatory variables, the model that would evidently provide the better fit is the one with a ________.
lower standard error of the estimate and a higher adjusted coefficient of determination
In a simple linear regression, an horizontal line suggests ____ linear relationship between x and y.
no
The R2 of a multiple regression of y on x1 and x2 measures the ________.
percentage of the variation in y that is explained by the sample regression equation
A regression model also allows us to make _____ regarding the response variable based on the known values of the explanatory variables.
predictions
A regression model also allows us to make ______ regarding the response variable based on the known values of the explanatory variables
predictions
Simple linear regression analysis differs from multiple regression analysis in that ________.
simple linear regression uses only one explanatory variable
A numerical measure that gauges the dispersion of data points from the sample regression equation is referred to as the ______.
standard error of the estimate
Using this distance measure, we say that the OLS method produces the ______ that is "closest" to the data.
straight line
The residual e represents
the difference between an observed and predicted value of the response variable at a given value of the explanatory variable.
SSR represents
the explained variation in the response variable Reason: "Sum of Squares" due to regression
Consider the following sample regression equation yˆy^ = 150 − 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). The slope coefficient indicates that if ________.
the price of Product A increases by $1, then we predict the demand to decrease by 20,000
SST represents the ______.
total variation in Y total sum of squares
The coefficient of determination R2 is ________.
usually higher than adjusted R2 R2 value always lie between 0 to 1. R2 value always rises when more variables are added but adjusted R2 can decreases. Usually R2 is higher than adjusted R2
Consider the following simple linear regression model: y = β0 + β1x + ε. The explanatory variable is ________.
x
Consider the simple linear regression model: y = β0 + β1x + ε Which symbol represents the explanatory variable?
x
What does the model y = β0 + β1 x + ε tell us about the relationship between the variables x and y?
x and y are linearly related, but the relationship is inexact, or stochastic.
Consider the following simple linear regression model: y = β0 + β1 + ε. The response variable is ________.
y
In a regression model, the residual e is calculated as ______.
y - ŷ
Consider the simple linear regression model: y = β0 + β1x + ε Which symbol represents the intercept?
β0
Consider the simple linear regression model: y = β0 + β1x + ε Which symbol represents random error?
ε
The standard error of the estimate is calculated as
√ErrorSumofSquares/n−k−1
