This document provides guided notes on inferences for correlation and regression. It discusses how the sample correlation coefficient and least squares line estimate population parameters and require assumptions about the data. It also outlines how to test the population correlation coefficient using a significance test and interpret the results. An example is provided testing the correlation between education levels and income growth. Students are asked to practice computing the standard error of estimate from a data set and answering summary questions.
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This is the information about biostatistics and there are various test which are performed in the laboratory to the field. these tests are f test chi square test etc. on the basis of these data we confirmed probability and calculation of variability. here is the whole information about the chi square test
Brief notes on heteroscedasticity, very helpful for those who are bigners to econometrics. i thought this course to the students of BS economics, these notes include all the necessary proofs.
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Chapter 10: Correlation and Regression
10.1: Correlation
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
This is the information about biostatistics and there are various test which are performed in the laboratory to the field. these tests are f test chi square test etc. on the basis of these data we confirmed probability and calculation of variability. here is the whole information about the chi square test
Brief notes on heteroscedasticity, very helpful for those who are bigners to econometrics. i thought this course to the students of BS economics, these notes include all the necessary proofs.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 10: Correlation and Regression
10.1: Correlation
Histograms and Descriptive Statistics Scoring GuideCRITERIANON.docxpooleavelina
Histograms and Descriptive Statistics Scoring Guide
CRITERIA
NON-PERFORMANCE
BASIC
PROFICIENT
DISTINGUISHED
Apply the appropriate SPSS procedures for creating histograms to generate relevant output.
Does not provide SPSS output.
Provides SPSS output with errors.
Applies the appropriate SPSS procedures for creating histograms to generate relevant output.
Analyzes the histogram output, demonstrating insight and understanding of relevant data.
Interpret histogram results, including concepts of skew, kurtosis, outliers, symmetry, and modality.
Does not provide an interpretation of histogram results.
Provides an interpretation of histogram results.
Interprets histogram results, including concepts of skew, kurtosis, outliers, symmetry, and modality.
Evaluates histogram results, including concepts of skew, kurtosis, outliers, symmetry, and modality.
Analyze the strengths and limitations of examining a distribution of scores with a histogram.
Does not identify the strengths and limitations of examining a distribution of scores with a histogram.
Identifies the strengths and limitations of examining a distribution of scores with a histogram.
Analyzes the strengths and limitations of examining a distribution of scores with a histogram.
Evaluates the strengths and limitations of examining a distribution of scores with a histogram. Demonstrates insight and understanding of relevant data.
Apply the appropriate SPSS procedure for generating descriptive statistics to generate relevant output.
Does not provide SPSS output.
Includes some, but not all, of the required output. Numerous errors in SPSS output.
Applies the appropriate SPSS procedure for generating descriptive statistics to generate relevant output.
Applies the appropriate SPSS procedure for generating descriptive statistics to generate relevant output. Includes all relevant output; no irrelevant output is included. No errors in SPSS output.
Analyze meaningful versus meaningless variables reported in descriptive statistics.
Does not identify meaningful versus meaningless variables reported in descriptive statistics.
Identifies meaningful versus meaningless variables reported in descriptive statistics.
Analyzes meaningful versus meaningless variables reported in descriptive statistics.
Evaluates meaningful versus meaningless variables reported in descriptive statistics.
Interpret descriptive statistics for meaningful variables.
Does not identify meaningful variables.
Identifies meaningful variables.
Interprets descriptive statistics for meaningful variables.
Evaluates descriptive statistics for meaningful variables.
Apply the appropriate SPSS procedures for creating z scores and descriptive statistics to generate relevant output.
Does not provide SPSS output.
Provides SPSS output with errors.
Applies the appropriate SPSS procedures for creating z scores and descriptive statistics to generate relevant output.
Analyzes the z scores and descriptive statistics output, demonstrating insight and understand ...
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1
To make tests of hypotheses about more than two population means, we use the:
t distribution
normal distribution
chi-square distribution
analysis of variance distribution
2
You randomly select two households and observe whether or not they own a telephone answering machine. Which of the following is a simple event?
At most one of them owns a telephone answering machine.
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1
To make tests of hypotheses about more than two population means, we use the:
t distribution
normal distribution
chi-square distribution
analysis of variance distribution
For more classes visit
www.snaptutorial.com
1
To make tests of hypotheses about more than two population means, we use the:
t distribution
normal distribution
chi-square distribution
analysis of variance distribution
1. AP/H Statistics Guided Notes
Mrs. LeBlanc – Perrone Name: ______________________________
9.3 Inferences for Correlation and Regression Date: ___________
Part 1: Testing and the Standard Error of Estimate
Inferences for Correlation and Regression
In Sections 9.1 and 9.2, we learned how to compute the sample correlation coefficient and the least-
squares line using data from a sample.
o is only a _____________________________________________________________________
o is only a _____________________________________________________________
o What if we used all possible data pairs?
In theory, if we had the population of all (x, y) pairs, then we could compute the
_________________________________________________________(Greek letter rho)
and we could compute the __________________________________________________
________________________________________________________________________
Note the following:
Sample Statistic Population Parameter
Requirements for Statistical Inference
o To make inferences regarding correlation and linear regression, we need to be sure that
The set (x, y) of ordered pairs is a random sample from the population of all possible
such (x, y) pairs
For each fixed value of x, the y values have a normal distribution. All of the y
distributions have the same variance, and, for a given x value, the distribution of y values
has a mean that lies on the least-squares line. We also assume that for a fixed y, each x
has its own normal distribution. In most cases the results are still accurate if the
distributions are simply mound-shaped and symmetric and the y variances are
approximately equal.
o ____________________________________________________________________________________
____________________________________________________________________________________
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2. AP/H Statistics Guided Notes
Mrs. LeBlanc – Perrone
Testing the Correlation Coefficient
The first topic we want to study is the statistical significance of the sample correlation coefficient r.
To do this, we construct a statistical test of , the population correlation coefficient.
How to Test the population correlation coefficient
Let be the sample correlation coefficient computed using data pair ( )
1. Use the null hypothesis (x and y have _______________________________).
Use the context of the application to state the alternate hypothesis ( ).
State the level of significance .
2. Obtain a sample of data pairs and compute the sample test statistic
with degrees of freedom
3. Use the TI-83 or TI-84 to calculate the _____________________
_______________________________________________________________________
4. Conclude the test
If the P-values is , then reject
If the P-values is , then fail to reject
5. Interpret the results in the context of your application
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3. AP/H Statistics Guided Notes
Mrs. LeBlanc – Perrone
Example: Testing
Do college graduates have an improved chance at a better income? Is there a trend in the general population
to support the “learn more, earn more” statement? We suspect the population correlation is positive, let’s test
using a 1% level of significance. Consider the following variables: x = percentage of the population 25 or older
with at least four years of college and y = percentage growth in per capita income over the past seven years. A
random sample of six communities in Ohio gave the information shown
Caution: Although we have shown that x and y are positively correlated, we have not shown that an
increase in education causes an increase in earnings.
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4. AP/H Statistics Guided Notes
Mrs. LeBlanc – Perrone
You Try It!
A medical research team is studying the effect of a new drug on red blood cells. Let x be a random variable
representing milligrams of the drug given to a patient. Let y be a random variable representing red blood cells
per cubic milliliter of whole blood. A random sample of volunteer patients gave the following results.
x 9.2 10.1 9.0 12.5 8.8 9.1 9.5
y 5.0 4.8 4.5 5.7 5.1 4.6 4.2
Use a 1% level of significance to test the claim that
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5. AP/H Statistics Guided Notes
Mrs. LeBlanc – Perrone
Standard Error of Estimate
Sometimes a scatter diagram clearly ______________________________________________________
between x and y, but it can happen that the points are widely scattered about the least-squares line.
We need a method (besides just looking) for measuring the spread of a set of points about the least-
squares line. There are three common methods of measuring the spread.
o the coefficient of correlation
o the coefficient of determination
o ______________________________________________________
For the standard error of estimate, we use a measure of spread that is in some ways like the
standard deviation of measurements of a single variable. Let_________________________________
________________________________________________from the least-squares line.
Then y – is the difference between the y value of the data point (x, y) shown on the scatter diagram
(Figure 9-16) and the value of the point on the least-squares line with the same x value.
The quantity __________ is known as the ___________________. To avoid the difficulty of having
some positive and some negative values, we square the quantity (y – ).
Then we sum the squares and, for technical reasons, divide this sum by n – 2. Finally, we take the
square root to obtain the standard error of estimate, denoted by S .
e
Standard Error of Estimate = ______________________________________________
where and
Using the TI 83 & TI 84
1. STAT
2. TEST
3. LinRegTTest
The value for is given as
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6. AP/H Statistics Guided Notes
Mrs. LeBlanc – Perrone
Example
June and Jim are partners in the chemistry lab. Their assignment is to determine how much copper sulfate
(CuSO ) will dissolve in water at 10, 20, 30, 40, 50, 60, and 70°C.Their lab results are shown in Table 9-12,
4
where y is the weight in grams of copper sulfatethat will dissolve in 100 grams of water at x°C. Sketch a scatter
diagram, find the equation of the least-squares line, and compute
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7. AP/H Statistics Guided Notes
Mrs. LeBlanc – Perrone
Summary Questions
1. What does testing the population correlation coefficient show?
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
2. Complete 9.1 – 9.3 Graphing Calculator Exercises (including the “You Try It”)
“HOT” Question:
__________________________________________________________________________________________
__________________________________________________________________________________________
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