Test 4
A partial slope estimates differences between average values of observations y that match on the other explanatory variables.
true
The correlation between _______ is the largest. It is so much larger than the others because ___________
-Price and Width -calculating the amount of gold involves squaring the width.
Even though the equation fit in part (c) has a large R squared and both slopes are significantly different from zero, the estimated regression does not meet the conditions of the MRM. Explain why. Select all that apply.
-There is a very important variable missing from the model. -There is a pattern in the residuals.
These tests ________ with each other because the overall F-statistic of F-equals _______ is _______ at alpha equals 0.05, which is ________ true of the t-statistics.
-do not agree -statistically significant -not
Scatterplot of X2 on X1
Collinearity
Indirect effect of X2
Marginal slope of X1 on X2
Does the path diagram for the multiple regression offer a suggestion for the differences noticed in the previous questions?
No, because path diagrams do not tell the difference between changes to standard errors.
Direct effect of X 2
Partial slope for X2
Determine whether the correlation between file size and transfer time differs significantly from zero. Choose the correct answer below.
Reject H0. There is sufficient evidence that the correlation between file size and transfer time is not zero.
Determine what the standard deviation of residuals is in the simple regression model.
Se
Scatterplot of e on y(hat)
Similar variances
Scatterplot of e on y-hat
Similar variances
How are the confidence intervals for file size different? Select all that apply.
The partial slope confidence interval is substantially wider than the marginal slope confidence interval.
How does the residual plot show that the model has improved?
The residual plot has less of a pattern and exposes previously unknown outliers.
The intercept estimates how much the response changes on average with changes in the predictor.
The statement is false because it is the slope that indicates how much the response changes on average with changes in the predictor.
The horizontal distance between y and y(hat) is known as the residual and so takes its scale from the predictor.
The statement is false because residuals are vertical distances and they take their scale from the response.
In the ideal situation, the SRM assumes that observations of the explanatory variable are independent of one another.
The statement is false because the SRM assumes that the errors are independent.
Mark the following statement as true or false. If you believe that the statement is false, briefly say why you think it is false. In the ideal situation, the SRM assumes that observations of the explanatory variable are independent of one another.
The statement is false because the SRM assumes that the errors are independent.
The errors in the SRM are the deviations from the least squares regression line.
The statement is false because the errors are deviations from the population regression line.
The plot of the residuals on the predictor should show a linear pattern, with the data packed along a diagonal line.
The statement is false because the plot of the residuals on the predictor should lack patterns.
An increase in the observed sample size from 100 customers to 2 comma 500 customers in a study of promotion response using simple regression produces predictions that are five times as accurate.
The statement is false. A larger sample size leads to more precise estimates of B0 and B1 but not necessarily more accurate predictions.
The partial slope for an explanatory variable has to be smaller in absolute value than its marginal slope.
The statement is false. The partial slope for an explanatory variable can be exactly the same size as its marginal slope. This occurs when the explanatory variable is completely uncorrelated with all other explanatory variables.
The estimated value y(hat)=b0+b1x approximates the average value of the response when the explanatory variable equals x.
The statement is true
The sum of the fitted value y-hat plus the residual e is equal to the original data value y.
The statement is true
The sum of the fitted value y(hat) plus the residual e is equal to the original data value y.
The statement is true.
Mark the statement True or False. If you believe that a statement is false, briefly explain why you think it is false. The partial slope corresponds to the direct effect in a path diagram.
This statement is true.
The partial slope corresponds to the direct effect in a path diagram.
This statement is true.
Errors in the simple regression model (SRM) represent the net effect on the response of other variables that are not accounted for by the model.
True
Does the fit of this model meet the conditions of the MRM? Select all that apply.
Yes, all of the conditions are satisfied.
Do the relevant plots appear straight enough for multiple regression? Select all that apply.
Yes, all three plots look straight enough.
Identifies the intercept in a fitted line
b0
Identifies the slope in a fitted line
b1
Indirect effect of x2
marginal slope of x1 on x2
Percentage variation described by a fitted line
r^2
Determine what the ratio of b1 to its standard error is in the simple regression model.
t-stat
Determine what the ratio of b 1 to its standard error is in the simple regression model.
t-statistic
Symbol for the explanatory variable in a regression
x
Symbol for the response in a regression
y
Fitted value from an estimated regression equation
y-hat
Residual from an estimated regression equation
y-y(hat)
The simple regression model (SRM) requires that a histogram of the response should look like a normal distribution.
False, the histogram of the residuals should look like a normal distribution
A slope in a simple regression is known as a partial slope because it ignores the effects of other explanatory variables.
False; a marginal slope includes the effects of other explanatory variables.
Mark the following statement as True or False. If you believe that a statement is false, briefly explain why you think it is false. If the confidence interval for the marginal slope of Upper X 1 includes zero, then the confidence interval for its partial slope includes zero as well.
False; because the value of the marginal slope can take on any value relative to the partial slope, depending on the scenario. It's possible for the marginal slope to not even have the same sign as the partial slope.
Are there any unusual features in the data? Select all that apply
Yes, it is unusual that the data include only several lengths and widths.
Are there any unusual features in the data? Select all that apply.
Yes, it is unusual that the file sizes increased steadily over the day. This suggests that the explanatory variables are associated.
Do the relevant plots appear straight enough for multiple regression? Select all that apply.
Yes, the relevant plots look straight enough.