Concept explainers
a.
State whether the given statement is true or false.
a.
Answer to Problem 88E
The given statement is false.
Explanation of Solution
The statement is, if Model I is fit, the estimate for
Model I is as follows:
An unbiased estimator of
According to this, the estimate for
It is given that
From Model I, the value of
The degrees of freedom is as follows:
This indicates that the estimate for
Since the estimate for
b.
Explain whether the given statement is true or false.
b.
Answer to Problem 88E
The given statement is true.
Explanation of Solution
The fitted Model II is as follows:
To determine whether
The significance level is 0.01.
The test statistic is as follows:
Where,
Here,
Also, it is noticed that
Where,
The rejection region for this test is as follows:
Where,
The value of
According to this, if
If
Thus, the given statement is true.
c.
Check whether
c.
Answer to Problem 88E
The given statement is true.
Explanation of Solution
If there are k independent variables, then the fitted model is as follows:
It is known that
Where
Here, Model I contains four independent variables
Also Model II contains two independent variables
This indicates that the predicted value for
Where,
This means that
According to this, the given statement is true.
d.
Check whether
d.
Answer to Problem 88E
The given statement is false.
Explanation of Solution
It is known that an unbiased estimator for
Where,
Also
For Model I, it is seen that
Now, compute the values of
From Part (c), it is seen that
Therefore, the given statement is false.
e.
Check whether Model II is a reduction of Model I.
e.
Answer to Problem 88E
The statement istrue.
Explanation of Solution
Models I and II are as follows:
It is observed that Model II is a subset of Model I.
That is,
Therefore, the given statement is true.
f.
Check whether Model III is a reduction of Model I.
f.
Answer to Problem 88E
The given statement isfalse.
Explanation of Solution
Models I and III are as follows:
Here, Model III contains
Want to see more full solutions like this?
Chapter 11 Solutions
Mathematical Statistics with Applications
- The following table was generated from the sample data of 1010 junior high students regarding the average number of hours they are unsupervised per night, the average number of hours they play video games per night, and their final grades in their math class. The dependent variable is the final grade, the first independent variable (x1x1) is the number of hours unsupervised each night, and the second independent variable (x2x2) is the number of hours of video games each night. Coefficients Standard Error t-Stat p-value Intercept 64.49590764.495907 5.9533305.953330 10.83358510.833585 0.0000370.000037 Hours Unsupervised −0.974079−0.974079 1.1097971.109797 −0.877709−0.877709 0.4138620.413862 Hours Playing Video Games 4.9768084.976808 1.0636721.063672 4.6788924.678892 0.0034000.003400 Step 1 of 2: Write the multiple regression equation for the computer output given. Round your answers to three decimal places. Step 2 of 2: Indicate if any of the independent variables…arrow_forwardThe following table was generated from the sample data of 1010 junior high students regarding the average number of hours they are unsupervised per night, the average number of hours they play video games per night, and their final grades in their math class. The dependent variable is the final grade, the first independent variable (x1x1) is the number of hours unsupervised each night, and the second independent variable (x2x2) is the number of hours of video games each night. Coefficients Standard Error t-Stat p-value Intercept 57.968435 7.227955 8.020032 0.000201 Hours Unsupervised 5.131630 1.314283 3.904510 0.007943 Hours Playing Video Games 1.067855 1.615039 0.661194 0.533040 Write the multiple regression equation for the computer output given. Round your answers to three decimal places.arrow_forwardThe following table was generated from the sample data of 1010 junior high students regarding the average number of hours they are unsupervised per night, the average number of hours they play video games per night, and their final grades in their math class. The dependent variable is the final grade, the first independent variable (x1x1) is the number of hours unsupervised each night, and the second independent variable (x2x2) is the number of hours of video games each night. Coefficients Standard Error t-Stat p-value Intercept 57.968435 7.227955 8.020032 0.000201 Hours Unsupervised 5.131630 1.314283 3.904510 0.007943 Hours Playing Video Games 1.067855 1.615039 0.661194 0.533040 Indicate if any of the independent variables could be eliminated at thearrow_forward
- The management of a supermarket wants to find if there is a relationship between the number of times a specific product is promoted on the intercom system in the store(x) and the number of units of that product sold (y). To experiment, the management selected a product and promoted it on the intercom system for 7 days, recording the number of times this product was promoted each day and the number of units sold. Summaries of a study conducted gave the following results: ∑x=177, ∑y= 144, SSxx=809.4286, SSyy=261.7143, SSxy= 407.8571 a) Calculate the correlation coefficient (r) relating number of times this product was promoted each day and the number of units sold. b) Find the regression line.arrow_forwardA study was undertaken to determine whether there was a significant weight (in lb) loss after one year course of therapy for diabetes, and whether the amount of weight (in lb) loss was related to initial weight. The following table gives the initial weight (x) and weight after one year of therapy (y) for 16 newly diagnosed adult diabetic patients.arrow_forwardNine students held their breath, once after breathing normally and relaxing for one minute, and once after hyperventilating for one minute. The table indicates how long (in sec) they were able to hold their breath. Is there an association between the two variables?arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,