A group of students measure the length and width of a random sample of beans. They are interested in investigating the relationship between the length and width. Their summary statistics are displayed in the table below. All units, if applicable, are millimeters. Mean width: 7.5 Stdev width: 0.909 Mean height: 13.89 Stdev height: 1.708 Correlation coefficient: 0.7858 a) The students are interested in using the width of the beans to predict the height. Calculate the slope of the regression equation. b) Write the equation of the best-fit line that can be used to predict bean heights. Use x to represent width and y to represent height. c) What fraction of the variability in bean heights can be explained by the linear model of bean height vs width? Express your answer as a decimal.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A group of students measure the length and width of a random sample of beans. They are interested in investigating the relationship between the length and width. Their summary statistics are displayed in the table below. All units, if applicable, are millimeters.
| Mean width: | 7.5 |
| Stdev width: | 0.909 |
| Mean height: | 13.89 |
| Stdev height: | 1.708 |
| 0.7858 |
a) The students are interested in using the width of the beans to predict the height. Calculate the slope of the regression equation.
b) Write the equation of the best-fit line that can be used to predict bean heights. Use x to represent width and y to represent height.
c) What fraction of the variability in bean heights can be explained by the linear model of bean height vs width? Express your answer as a decimal.
d) If, instead, the students are interested in using the height of the beans to predict the width, calculate the slope of this new regression equation.
e) Write the equation of the best-fit line that can be used to predict bean widths. Use x to represent height and y to represent width.
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