1. When doing regression analysis, we draw a scatterplot to check the form of th
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1. When doing regression analysis, we draw a scatterplot to check the form of the relationship (linear or nonlinear). We also have to check for influential observations. In Figure 14.12 (p. 640), the influential observation is the top left-most point. The regression equation changes considerably if this point is removed from the analysis. When do we usually find influential observations?
a.
when the response variable is not normally distributed
b.
when a data point is separated in the horizontal direction from the other points and there are no other data points below or above the point in question
c.
when the point is near the mean value of the predictor variable
d.
when the relationship between the predictor and response variables is weak
2. Consider the linear regression model:
BODY FATi = 0 + 1ABDOMENi + i
Here ABDOMEN is measured in inches and BODY FAT is percentage of body fat.
Suppose ABDOMEN = 35 inches. Which statement is correct?
a.
BODY FAT is 0 + 1(35).
b.
Mean BODY FAT is 0 + 1(35).
c.
Mean BODY FAT is 0 + 1(35) + i.
d.
(a) and (c) are correct.
3. Consider the linear regression model:
BODY FATi = 0 + 1ABDOMENi + i
Here ABDOMEN is measured in inches and BODY FAT is percentage of body fat.
Which statistic do we use to estimate the regression variance 2?
a.
Root MSE
b.
MSE
c.
0-hat
d.
1-hat
4. Consider the linear regression model:
BODY FATi = 0 + 1ABDOMENi + i
Here ABDOMEN is measured in inches and BODY FAT is percentage of body fat.
Which of the following statements illustrates the linearity assumption?
a.
The BODY FAT of an individual can be perfectly predicted by ABDOMEN.
b.
The BODY FAT variance when ABDOMEN = 35 inches, the BODY FAT variance when ABDOMEN = 40 inches and the BODY FAT variance when ABDOMEN = 30 inches all lie on a line.
c.
When ABDOMEN = 35 inches, there is only one BODY FAT value. When ABDOMEN = 40 inches, there is also one BODY FAT value. When ABDOMEN = 30 inches, there is also one BODY FAT value. Although the BODY FAT values are different, they all lie on a line.
d.
The mean BODY FAT when ABDOMEN = 35 inches, the mean BODY FAT when ABDOMEN = 40 inches and the mean BODY FAT when ABDOMEN = 30 inches all lie on a line.
5. Consider the linear regression model:
BODY FATi = 0 + 1ABDOMENi + i
Here ABDOMEN is measured in inches and BODY FAT is percentage of body fat.
In which situation is the independence assumption not satisfied?
a.
when the linear regression model contains independent variables that are categorical
b.
when the linear regression model contains a dependent variable that is categorical
c.
when the data consist of repeated measurements from the same individuals
d.
when the data consist of correlated independent variables
a.
when the response variable is not normally distributed
b.
when a data point is separated in the horizontal direction from the other points and there are no other data points below or above the point in question
c.
when the point is near the mean value of the predictor variable
d.
when the relationship between the predictor and response variables is weak
640 CHAPTER 14 Descriptive Methods in Regression and Correlation To help avoid extrapolation, some researchers include the range of the observ values of the predictor variable with the regression equation. For the Orion ex we would write 195.47 20.26x Writing the regression equation in this way makes clear that using it to predict for ages outside the range from 2 to 7 years old is extrapolation Outliers and Influential Observations Recall that an outlieris an observation that lies outside the overall pattern ofthe data the context of regression, an outlier is a data point that lies far from the regression line relative to the other data points. Figure l4.10 on page 638 shows that the Orio have no outliers An outlier can sometimes have a significant effect on a regression analysis. Th as usual, we need to identify outliers and remove them from the analysis APPLET appropriate for example, if we find that an outlier is a measurement or rec Applet 14.2 error. We must also watch for influential observations. In regression analysis, an ential observation is a data point whose removal causes the regression equation line) to change considerably. A data point separated in the x-direction from the data points is often an influential observation because the regression line is toward such a data point without counteraction by other data points If an influential observation is due to a measurement or recording error, o if im some other reason it clearly does not belong n the data set, it can be removed wi out further consideration. However, if no explanation for the influential observa apparent, the decision whether to retain itis often difficult and calls for a judgment the researcher For the Orion data, Fig 4.10 on page 638 (or Table 14.5 on page 637) shou that the data point (2, 169) might be an influential observation because the age 2 years appears separated from the other observed ages. Removing that data poin and recalculating the regression equation yields 60.33 4.24x. Figure 14. reveals that this equation differs markedly from the regression equation based on full data set. The data point (2, 169) is indeed an influential observation. FIGURE 14.12 Regression lines with and withou Influential observation 180 the influential observatio removed 70 60 50 195.47 -20.26x 40 (based on all data) 30 20 110 100 90 80 160.33 14.24x 70 (influential observation 60 removed from data) 50 40 30 20 10 Age (y The influential observation (2,169) is not a recording error; it is a legitimate dau point. Nonetheless, we may need either to remove it. limiting the analysis Orions between 4 and 7 years old-or to obtain additional data on 2- and 3 de Orions so that the regression analysis is not so dependent on one data point We added data for one 2-year-old and three 3-year-old Orions and obtain the regression equation 193.63 19.93x. This regression equation differs little fronExplanation / Answer
ques.1:
(D) is correct answer
An influential observation is an observation for a statistical calculation whose deletion from the dataset would noticeably change the result of the calculation. In particular, in regression analysis an influential point is one whose deletion has a large effect on the parameter estimates.
ques 2:
(A) is correct .
as regression model shows relationship between variables (either degree of dependency or if variable are dependent or not rate of change in one variable cause change in other variables irrespective of units)
ques 3:
(B) is correct answer
as MSE as residual error we got from ANOVA(analysis of variance ) is population variance
ques 4:
(A) is true ,as we are assuming the abodomen can perfectly predict body fat.
ques. 5
(D) is correct, as assumptions states there should not be multicollinearity between independent variables,thus we need to eliminate multicollinearity so that assumptions can be satisfied
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