Podcast
Questions and Answers
Using Scenario 12-1, which condition for inference requires further analysis of the data to confirm it has been satisfied, beyond the information already provided to confirm the other four conditions for slope inference?
Using Scenario 12-1, which condition for inference requires further analysis of the data to confirm it has been satisfied, beyond the information already provided to confirm the other four conditions for slope inference?
- For each value of Freshman GPA, the distribution of Senior GPA is roughly Normal.
- The mean Senior GPA is a linear function of Freshman GPA.
- The standard deviation of Senior GPA is roughly equal for each value of Freshman GPA. (correct)
- Observations for each student are independent.
Based on Scenario 12-3 and the residual plot provided, which condition for inference is most likely NOT satisfied?
Based on Scenario 12-3 and the residual plot provided, which condition for inference is most likely NOT satisfied?
- For each value of English rating, the distribution of history rating is roughly Normal.
- Observations for each student are independent.
- The data come from a random sample.
- The standard deviation of history rating is roughly equal for each value of English rating. (correct)
In Scenario 12-3, which condition for inference should be checked by examining a Normal Probability plot of the residuals?
In Scenario 12-3, which condition for inference should be checked by examining a Normal Probability plot of the residuals?
- The data come from a random sample.
- Observations for each student are independent.
- The standard deviation of history rating is roughly equal for each value of English rating.
- For each value of English rating, the distribution of history rating is roughly Normal. (correct)
Assuming the conditions for inference have been met in Scenario 12-3, how many degrees of freedom are associated with the t-statistic's distribution when performing a t-test for the regression slope?
Assuming the conditions for inference have been met in Scenario 12-3, how many degrees of freedom are associated with the t-statistic's distribution when performing a t-test for the regression slope?
Referring to Scenario 12-3, what is the test statistic for performing a t-test for the regression slope?
Referring to Scenario 12-3, what is the test statistic for performing a t-test for the regression slope?
Using Scenario 12-3, and assuming that the conditions for inference have been met, which of the following represents a 99% confidence interval for the rate of change in history rating for a one-unit change in English rating?
Using Scenario 12-3, and assuming that the conditions for inference have been met, which of the following represents a 99% confidence interval for the rate of change in history rating for a one-unit change in English rating?
In Scenario 12-4, which of the following provides the correct interpretation of s = 0.355761?
In Scenario 12-4, which of the following provides the correct interpretation of s = 0.355761?
Referring to Scenario 12-6, what does the quantity R-Sq = 19.8% represent?
Referring to Scenario 12-6, what does the quantity R-Sq = 19.8% represent?
Suppose you measure a response variable Y for several values of an explanatory variable X. If a scatterplot of log Y versus log X looks approximately like a negatively-sloping straight line, what can you conclude about the relationship between Y and X?
Suppose you measure a response variable Y for several values of an explanatory variable X. If a scatterplot of log Y versus log X looks approximately like a negatively-sloping straight line, what can you conclude about the relationship between Y and X?
Suppose the relationship between a response variable y and an explanatory variable x is modeled well by the equation $y = 3.6(0.32)^x$. Which of the following plots is most likely to be roughly linear?
Suppose the relationship between a response variable y and an explanatory variable x is modeled well by the equation $y = 3.6(0.32)^x$. Which of the following plots is most likely to be roughly linear?
Flashcards
Condition needing further analysis in Scenario 12-1?
Condition needing further analysis in Scenario 12-1?
The fifth condition requiring further analysis is whether, for each value of Freshman GPA, the distribution of Senior GPA is roughly Normal.
What does the residual plot suggest in scenario 12-3?
What does the residual plot suggest in scenario 12-3?
The residual plot can indicate whether the standard deviation of the history rating is roughly equal for each value of the English rating.
How to check the condition for inference in scenario 12-3?
How to check the condition for inference in scenario 12-3?
To check this condition, examine a Normal Probability plot of the residuals.
Degrees of freedom for the t-statistic's distribution in scenario 12-3?
Degrees of freedom for the t-statistic's distribution in scenario 12-3?
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What is the test statistic for the t-test in scenario 12-3?
What is the test statistic for the t-test in scenario 12-3?
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Correct interpretation of s in Scenario 12-4?
Correct interpretation of s in Scenario 12-4?
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What does R-Sq = 19.8% represent?
What does R-Sq = 19.8% represent?
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What model describes the relationship between Y and X?
What model describes the relationship between Y and X?
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Plot to check if y=3.6(0.32)^x is linear?
Plot to check if y=3.6(0.32)^x is linear?
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What model and equation are given by the printout?
What model and equation are given by the printout?
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Study Notes
- Practice Questions for Chapter 12 on statistics concepts and applications
Scenario 12-1: Predicting GPA
- A high school counselor aims to predict senior year GPA based on freshman year GPA.
- A random sample of 15 seniors from a class of 468 are analyzed.
- 'Senior' represents full-year GPA in senior year, and 'Fresh' represents first-marking-period GPA in freshman year.
- Regression analysis results:
- Constant: Coef = 1.6310, SE Coef = 0.5328, T = 3.06, P = 0.009
- Fresh: Coef = 0.5304, SE Coef = 0.1789, T = 2.96, P = 0.011
- S = 0.3558, R-Sq = 40.3%, R-Sq(adj) = 35.7%
- A residual plot is provided for senior vs. fresh regression.
- For slope inference, further analysis is needed to confirm the condition that for each value of Freshman GPA, the distribution of Senior GPA is roughly Normal.
Scenario 12-3: English and History Enjoyment
- Examines if students who like English also enjoy history.
- Data from 30 students is analyzed from a Canada Census at Schools survey performed in 2004-5.
- Students rated their liking of English and history on a scale of 0 to 5.
- Regression analysis results:
- Constant: Coef = 1.1867, SE Coef = 0.5574, T = 2.13, P = 0.042
- English: Coef = 0.5254, SE Coef = 0.1995, T = 2.63, P = 0.014
- S = 1.37707, R-Sq = 19.8%, R-Sq(adj) = 17.0%
- A residual plot for history rating vs. english rating is given.
- The residual plot suggests that the condition that has not been satisfied for inference is that the standard deviation of history rating is roughly equal for each value of English rating.
T-test for Regression Slope
- Assuming conditions for inference are met in Scenario 12-3, a t-test for regression slope has 28 degrees of freedom.
- Under Scenario 12-3, the test statistic for performing a t-test for regression slope is 2.63.
- A 99% confidence interval for the rate of change in history rating for a one-unit change in English rating is represented by 0.5254±2.763 (0.1995/√28)
Scenario 12-4
- A high school guidance counselor aims to predict senior year GPA based on freshman year GPA.
- A random sample of 15 seniors from a class of 468 are analyzed.
- 'Senior' represents full-year GPA in senior year, and 'Fresh' represents first-marking-period GPA in freshman year.
- The conditions for regression inference have been satisfied.
- Regression analysis results:
- Constant: Coef = 1.6310, SE Coef = 0.5328, T = 3.06, P = 0.009
- Fresh: Coef = 0.5304, SE Coef = 0.1789, T = 2.96, P = 0.011
- S = 0.355761 R-Sq = 40.3% R-Sq(adj) = 35.7%
- An interpretation of s = 0.355761 is that Predictions of Senior GPA from Freshman GPA based on this regression model will be off by an average of about 0.355761.
Scenario 12-6
- Examines if students who like English also enjoy history.
- Data from 30 students is analyzed from a Canada Census at Schools survey performed in 2004-5.
- Students rated their liking of English and history on a scale of 0 to 5.
- R-Sq = 19.8% represents the percentage of variation in history rating that can be explained by the regression of history rating on English rating
Relationships Between Variables
- If a scatterplot of log Y versus log X looks approximately like a negatively-sloping straight line, a power model would approximately describe the relationship between Y and X. -Given the equation y=3.6(0.32)^x, the plot of log y against x is most likely to be roughly linear.
Scenario 12-7: Marine Crustaceans Digestion
- Examines food assimilation in marine crustaceans.
- The percentage of food eaten that is assimilated decreases as food eaten increases.
- A scatterplot of In Assimilation versus In Food Intake is strongly linear.
- Regression analysis results:
- Constant: Coef = 6.3324, SE Coef = 0.5218, T = 12.14, P = 0.000
- In Food Intake: Coef = -0.6513, SE Coef = 0.1047, T = -6.22, P = 0.000
- s = 0.247460, R-Sq = 84.7%, R-Sq(adj) = 82.5%
- The model given is a power model with equation Assimilation = 6.3324-0.6513 (In Food Intake)
Scenario 12-9
- In Scenario 12-9, when food intake is 250 µg/day, the predicted assimilation rate from the above model is 27.4%.
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