Is the data point, P, an outlier, an influential point,
both, or neither?
Outlier
Neither
Both
Influential point
Question 2
Construct a scatterplot and identify the mathematical
model that best fits the data. Assume that the model is to be used
only for the scope of the given data and consider only linear,
quadratic, logarithmic, exponential, and power models. Use a
calculator or computer to obtain the regression equation of the
model that best fits the data. You may need to fit several models
and compare the values of R2.
A rock is dropped from a tall building and its distance (in feet)
below the point of release is recorded as accurately as possible at
various times after the moment of release. The results are shown in
the table. Find the regression equation of the best model.
y = 13.0 e0.686 x
y = -74.9 + 290 ln x
y = – 148.4 + 112 x
y = 15.95 x2
Question 3
Suppose you will perform a test to determine whether
there is sufficient evidence to support a claim of a linear
correlation between two variables. Find the critical values of r
given the number of pairs of data n and the significance level .
n = 12, = 0.05
r = ±0.576
r = 0.576
r = ±0.708
r = 0.602
Question 4
Use the given information to find the coefficient of
determination.
Find the coefficient of determination, given that the value of the
linear correlation coefficient, r, is 0.419.
0.824
0.419
0.176
0.581
Question 5
Suppose you will perform a test to determine whether
there is sufficient evidence to support a claim of a linear
correlation between two variables. Find the critical values of r
given the number of pairs of data n and the significance level .
n = 17, = 0.01
r = ±0.482
r = ±0.606
r = 0.606
r = 0.623
Question 6
Suppose you will perform a test to determine whether
there is sufficient evidence to support a claim of a linear
correlation between two variables. Find the critical values of r
given the number of pairs of data n and the significance level .
n = 17, = 0.05
r = ±0.482
r = 0.482
r = ±0.606
r = 0.497
Question 7
Find the total variation for the paired
data.
The equation of the regression line for the paired data below is . Find the total variation.
6,531.37
6,544.86
13.479
6,693.27
Question 8
Is the data point, P, an outlier, an influential point,
both, or neither?
The regression equation for a set of paired data is = 10 + 2x. The correlation coefficient for
the data is 0.93. A new data point, , is added to the set.
Neither
Influential point
Outlier
Both
Question 9
Find the unexplained variation for the paired
data.
The equation of the regression line for the paired data below is . Find the unexplained variation.
14.25
88.75
10.00
78.75
Question 10
Suppose you will perform a test to determine whether
there is sufficient evidence to support a claim of a linear
correlation between two variables. Find the critical values of r
given the number of pairs of data n and the significance level .
n = 11, = 0.01
r = 0.765
r = ±0.735
r = 0.735
r = ±0.602
Question 11
Use the given data to find the best predicted value of
the response variable.
The regression equation relating attitude rating (x) and job
performance rating (y) for the employees of a company is Ten pairs of data were used to obtain the
equation. The same data yield and What is the best predicted job performance
rating for a person whose attitude rating is 77?
80.1
88.9
90.2
12.6
Question 12
Find the unexplained variation for the paired
data.
The paired data below consists of test scores and hours of
preparation for 5 randomly selected students. The equation of the
regression line is . Find the unexplained variation.
87.4757
511.724
96.103
599.2
Question 13
Use the given data to find the best predicted value of
the response variable.
The regression equation relating dexterity scores (x) and
productivity scores (y) for the employees of a company is Ten pairs of data were used to obtain the
equation. The same data yield and What is the best predicted productivity
score for a person whose dexterity score is ?
56.30
72.35
194.41
58.20
Question 14
Construct a scatterplot and identify the mathematical
model that best fits the data. Assume that the model is to be used
only for the scope of the given data and consider only linear,
quadratic, logarithmic, exponential, and power models. Use a
calculator or computer to obtain the regression equation of the
model that best fits the data. You may need to fit several models
and compare the values of R2.
y = 7.19 + 12.8 ln x
y = 6.81 e0.316x
y = 4.40 + 5.00 x
y = 7.82 x0.844
Question 15
Use the given information to find the coefficient of
determination.
Find the coefficient of determination, given that the value of the
linear correlation coefficient, r, is 0.299.
0.911
0.701
0.089
0.299
Question 16
Find the unexplained variation for the paired
data.
The paired data below consists of heights and weights of 6 randomly
selected adults. The equation of the regression line is . Find the unexplained variation.
979.44
100.06
119.3
1079.5
Question 17
Use the given data to find the best predicted value of
the response variable.
Six pairs of data yield r = 0.789 and the regression equation Also, What is the best predicted value of y for ?
22.0
18.0
19.0
18.5
Question 18
Find the value of the linear correlation coefficient
r.
The paired data below consist of the test scores of 6 randomly
selected students and the number of hours they studied for the
test.
0.678
-0.678
0.224
-0.224
Question 19
Use the given information to find the coefficient of
determination.
A regression equation is obtained for a collection of paired data.
It is found that the total variation is 28.057, the explained
variation is 17.849, and the unexplained variation is 10.208. Find
the coefficient of determination.
1.572
0.364
0.572
0.636
Question 20
Use computer software to obtain the multiple regression
equation. Use the estimated equation to find the predicted
value.
A health specialist gathered the data in the table to see if pulse
rates can be explained by exercise and smoking. For exercise, he
assigns 1 for yes, 2 for no. For smoking, he assigns 1 for yes, 2
for no. He then used his results to predict the pulse rate of a
person whose exercise value was 1 and whose smoking value was
1.
74 beats/min
77 beats/min
70 beats/min
81 beats/min
Question 21
Use the computer display to answer the
question.
A collection of paired data consists of the number of years that
students have studied Spanish and their scores on a Spanish
language proficiency test. A computer program was used to obtain
the least squares linear regression line and the computer output is
shown below. Along with the paired sample data, the program was
also given an x value of 2 (years of study) to be used for
predicting test score.
If a person studies 4.5 years, what is the single value that is the
best predicted test score? Assume that there is a significant
linear correlation between years of study and test score.
49.1
80.6
83.0
53.35
Question 22
Solve the problem.
After obtaining a regression line y = 0 + 1x , a confidence interval for the mean of
all values y for which x = x0 can be obtained as follows:
The critical value t/2 is found from the t-table using n – 2
degrees of freedom.
Use the data below to obtain a 95% confidence interval estimate of
the mean test score of all students who study 10.5 hours. Note that
the equation of the regression line is and that
