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Questions and Answers
Which of the following is the estimate from this sample of the standard deviation of the sampling distribution of b, the slope of the sample regression line for this relationship?
Which of the following is the estimate from this sample of the standard deviation of the sampling distribution of b, the slope of the sample regression line for this relationship?
- 20.50
- 30.00
- 28.80 (correct)
- 25.60
Which of the following is the best interpretation of the quantity of s = 145.851?
Which of the following is the best interpretation of the quantity of s = 145.851?
- The average file size is 145.851 KB
- Predictions will be accurate within 145.851 KB
- 145.851 is the maximum file size expected
- Predictions of word count from file size based on this regression model will be off by an average of about 145 KB (correct)
If the teacher uses these data to test the hypothesis Ho: B = 0 versus Ha: B ≠0 at the 0.05 level, which of the following is an appropriate conclusion?
If the teacher uses these data to test the hypothesis Ho: B = 0 versus Ha: B ≠0 at the 0.05 level, which of the following is an appropriate conclusion?
- There is not enough information to make a conclusion.
- We cannot reject Ho since the p-value is too high.
- Since the p-value of 0.075 is less than 0.05, we reject Ho.
- Since the p-value of 0.022 is less than 0.05, we reject Ho. (correct)
Which of the following conditions must be satisfied in order to perform inference for regression of y on x?
Which of the following conditions must be satisfied in order to perform inference for regression of y on x?
Which of the following is an appropriate interpretation of the number 0.092498?
Which of the following is an appropriate interpretation of the number 0.092498?
Which of the following expressions best represents the margin of error of a 90% confidence interval for the slope of the population regression line?
Which of the following expressions best represents the margin of error of a 90% confidence interval for the slope of the population regression line?
Based on this residual plot, which of the following statements is true?
Based on this residual plot, which of the following statements is true?
The scatterplot of log (number of employees) versus year shows a strong, positive, linear pattern. Which of the following conclusions can be drawn from this information?
The scatterplot of log (number of employees) versus year shows a strong, positive, linear pattern. Which of the following conclusions can be drawn from this information?
A fisheries research report gives... Which of the following is closest to the predicted weight of a gracile lizardfish that was 12 cm long, based on this model?
A fisheries research report gives... Which of the following is closest to the predicted weight of a gracile lizardfish that was 12 cm long, based on this model?
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Study Notes
Standard Deviation of Sampling Distribution
- The estimated standard deviation of the sampling distribution of the slope (b) for the regression line is 28.80.
Average Prediction Error
- The quantity s = 145.851 indicates that predictions of word count from file size based on the regression model will have an average error of approximately 146 KB.
Hypothesis Testing Conclusion
- At the 0.05 significance level, with a p-value of 0.022, the null hypothesis ( H_0: B = 0 ) is rejected. This provides convincing evidence of a linear relationship between file size and word count.
Inference Conditions for Regression
- To perform inference for regression of y on x, two conditions must be met:
- The population of y-values for each x value has the same standard deviation.
- There is a linear relationship between x and the mean value of y for each x value.
Interpretation of Coefficient
- The coefficient 0.092498 means that for every increase of $100,000 in sales, predicted profits increase by $9,249.80.
Margin of Error for Confidence Interval
- The margin of error for a 90% confidence interval for the slope of the population regression line can be represented as 1.686(0.0106).
Residual Plot Interpretation
- Analyzing the residual plot, it can be concluded that:
- The relationship between the number of employees and year is non-linear.
- The regression equation would likely overestimate the number of employees at Microsoft in 1982.
Scatterplot Conclusion
- A strong positive linear pattern in the scatterplot of log(number of employees) versus year suggests that the relationship can be effectively modeled using an exponential function.
Correct Regression Equation
- From the regression analysis of log(number of employees) at Microsoft and Year, the correct regression equation is ( \log(y) = -449.7 + 0.228x ).
Prediction for Gracile Lizardfish
- The predicted weight for a gracile lizardfish measuring 12 cm in length, based on the given model, is approximately 13.89 grams.
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