STT 231 EXAM 1 WITH 100% CORRECT
ANSWERS
What are residual values in relation to the linear regression model? - Answer- -Values
explain by how much predicted values deviate from observed Y-values.
-If e=0, then there are no errors
-If e=+value, then predicted value is an underestimation
-If e=-value, then predicted value is an overestimation
What is the coefficient of determination? - Answer- R^2 value. Measures the fraction of
total sample variation in y explained by regression model. The larger the value, the
better the fit (e.g. 89% of total sample variation is explained by the model).
A study of class attendance and grades among first year students at a state university
showed that in general students who attended a higher percent of their classes earned
higher grades. Class attendance explained 16% of the variation in grade index among
the students. What is the correlation between attendance and grade index? - Answer-
r=0.4 (because R^2=16%)
Since the number of students could be different and the standard deviations could be
different the investigator decided to standardize the scores. That is instead of the actual
score in exam 1 for a student he used the corresponding z-score. This was done for all
the scores in all the exams resulting in the lines:
for the 300 level: zy=0+ 0.71 zx
for the 400 level: zy=0+ 0.65 zx - Answer- Correlation between the two exams for the
300 level courses is larger than that for the 400 level course.
You asked ten of your classmates about their weight. On the basis of this information,
you stated that the average weight of all students in your university or college is 142.6
pounds. This is an example of: - Answer- statistic
A company has developed a new battery, but the average lifetime is unknown. In order
to estimate this average, a sample of 100 batteries is tested and the average lifetime of
this sample is found to be 250 hours. Identify population, sample, variable, parameter,
and statistic. - Answer- -Population: all new batteries
-Sample: 100 tested batteries
-Variable: battery lifetime
-Parameter: average of all tested batteries
-Statistic: average of 250 hours
ANSWERS
What are residual values in relation to the linear regression model? - Answer- -Values
explain by how much predicted values deviate from observed Y-values.
-If e=0, then there are no errors
-If e=+value, then predicted value is an underestimation
-If e=-value, then predicted value is an overestimation
What is the coefficient of determination? - Answer- R^2 value. Measures the fraction of
total sample variation in y explained by regression model. The larger the value, the
better the fit (e.g. 89% of total sample variation is explained by the model).
A study of class attendance and grades among first year students at a state university
showed that in general students who attended a higher percent of their classes earned
higher grades. Class attendance explained 16% of the variation in grade index among
the students. What is the correlation between attendance and grade index? - Answer-
r=0.4 (because R^2=16%)
Since the number of students could be different and the standard deviations could be
different the investigator decided to standardize the scores. That is instead of the actual
score in exam 1 for a student he used the corresponding z-score. This was done for all
the scores in all the exams resulting in the lines:
for the 300 level: zy=0+ 0.71 zx
for the 400 level: zy=0+ 0.65 zx - Answer- Correlation between the two exams for the
300 level courses is larger than that for the 400 level course.
You asked ten of your classmates about their weight. On the basis of this information,
you stated that the average weight of all students in your university or college is 142.6
pounds. This is an example of: - Answer- statistic
A company has developed a new battery, but the average lifetime is unknown. In order
to estimate this average, a sample of 100 batteries is tested and the average lifetime of
this sample is found to be 250 hours. Identify population, sample, variable, parameter,
and statistic. - Answer- -Population: all new batteries
-Sample: 100 tested batteries
-Variable: battery lifetime
-Parameter: average of all tested batteries
-Statistic: average of 250 hours
