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Indicate Independent and Dependent Variables

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1. Indicate which would be the independent variable and which would be the dependent variable in each of the following:
a. Score on the first test, Final grade
b. Gas mileage, Car speed
c. High school grade point average, Freshman College grade point average
d. Crop yield, Rainfall
2. A math test was given with the following results:
80, 69, 92, 75, 88, 37, 98, 92, 90, 81, 32, 50, 59, 66, 67, 66
Find the range, standard deviation, and variance for the scores.
3. For a particular sample of 50 scores on a psychology exam, the following results were obtained.
Mean = 78 Midrange = 72 Third quartile = 94 Mode = 84
Median = 80 Standard deviation = 11 Range = 52 First quartile = 68
a. What score was earned by more students than any other score? Why?
b. How many students scored between 68 and 94 on the exam?
c. What was the highest score earned on the exam?
d. What was the lowest score earned on the exam?
e. How many students scored within three standard deviations of the mean ?
4. Answer the following:
a. What does it mean to say that x = 152 has a standard score of +1.5?
b. What does it mean to say that a particular value of x has a z-score of -2.1?
c. In general, what is the standard score a measure of?
5. A student scored 70 percent on a test, and was in the 80th percentile. Explain these two numbers.
6. An animal trainer obtained the following data (Table A) in a study of reaction times of dogs (in seconds) to a specific stimulus. He then selected another group of dogs that were much older than the first group and measure their reaction times to the same stimulus. The data is shown in Table B.
Table A Table B
Find the variance and standard deviation for the two distributions above. Compare the variation of the data sets. Decide if one data set is more variable than the other.
7. Answer the following:
a. What is the relationship between the sign of the correlation coefficient and the sign of the slope of the regression line?
b. As the value of the correlation coefficient increases from 0 to 1, or decreases from 0 to -1, how do the points of the scatter plot fit the regression line?
8. Describe in your own words what is meant by "line of best fit".
9. In your own words, state the primary purpose of:
a. linear correlation analysis
b. regression analysis
10. You are given the following data.
Number of Absences Final
Grade
0 96
1 91
2 78
2 83
3 75
3 62
4 70
5 68
6 56
a. Make a scatter plot for the data.
b. Find the correlation coefficient for the data.
c. Find the equation for the regression line for the data, and predict the final grade of a student who misses 3.5 days.

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https://brainmass.com/statistics/quantative-analysis-of-data/indicate-independent-dependent-variables-141095

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Solution Summary

This posting provides solution to statistics problems including identification of dependent variable and independent variable, standard deviation, probability, correlation coefficient, line of best fit, slope of regression line, scatter plot etc.

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Regression Study Questions

1. What is the variable used to predict the value of another called?

A) Independent
B) Dependent
C) Correlation
D) Determination

2. Based on the regression equation, we can

A) predict the value of the dependent variable given a value of the independent variable.
B) predict the value of the independent variable given a value of the dependent variable.
C) measure the association between two variables.

3. What is the range of values for a coefficient of correlation?

A) 0 to +1.0
B) -3 to +3 inclusive
C) -1.0 to +1.0 inclusive
D) Unlimited range

4. What is the general form of the regression equation?

A) Y' = ab
B) Y' = a + bX
C) Y' = a - bX
D) Y' = abX

5. Which value of r indicates a stronger correlation than 0.40?

A) -0.30
B) -0.50
C) +0.38
D) 0

6. Suppose the least squares regression equation is Y' = 1202 + 1133X.
When X = 3, what does Y' equal?

A) 5,734
B) 8,000
C) 4,601
D) 4,050

7. In the least squares equation, Y' = 10 + 20X the value of 20 indicates

A) the Y intercept.
B) for each unit increase in X, Y increases by 20.
C) for each unit increase in Y, X increases by 20.

8. In the equation Y' = a + bX, what is Y'?

A) Slope of the line
B) Y intercept
C) Predicted value of Y, given a specific X value
D) Value of Y when X=0

9. In the equation Y' = a + bX, what is a?

A) Slope of the line
B) Y intercept
C) Predicted value of Y, given a specific X value
D) Value of Y when X=0

10. If the regression equation is Y' = 2 - 0.4X, what is the value of Y' when X = -3?

A) 0.8
B) 3.2
C) -10.0
D) 14.0

11. In the regression equation, y' = a + bx what does the letter "b" represent?

A) Y intercept
B) Slope of the line
C) Any value of the independent variable that is selected
D) Value of Y when X=0

12. A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales. What is the dependent variable?

A) Salesperson
B) Number of contacts
C) Amount of sales
D) All the above

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