Verified step by step guidance
05:43
07:09 05:43"Constructing and Interpreting a Prediction Interval In Exercises 21-30, construct the indicated prediction interval and interpret the results.
26. Voter Turnout Construct a 99% prediction interval for number of ballots cast in Exercise 16 when the voting age population is 210 million."
"In Exercises 7-10, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?
10. r =0.881"
"Confidence Intervals for y-Intercept and Slope
You can construct confidence intervals for the y-intercept B and slope M of the regression line y = Mx + B for the population by using the inequalities below.
y-intercept B :
b - E < B < b + E
where
E = t_c s_e \(\sqrt{\frac{1}{n}\) + \(\frac{\overline{x}\)^2}{\(\sum\) x^2 - \(\frac{(\Sigma x)^2}{n}\)}}
slope M :
m - E < M < m + E
where
E = \(\frac{t_c s_e}{\sqrt{\sum x^2 - \frac{(\Sigma x)^2}{n}\)}}
The values of m and b are obtained from the sample data, and the critical value t_c is found using Table 5 in Appendix B with n - 2 degrees of freedom.
In Exercises 37 and 38, construct the indicated confidence intervals for B and M using the gross domestic products and carbon dioxide emissions data found in Example 2.
38. 99% confidence interval"
"Predicting y-Values In Exercises 3-6, use the multiple regression equation to predict the y-values for the values of the independent variables.
5. Black Cherry Tree Volume The volume (in cubic feet) of a black cherry tree can be modeled by the equation
y =- 52.2+0.3x_1 +4.5x_2
where x_1 is the tree's height (in feet) and x_2 is the tree's diameter (in inches). (Source: Journal of the Royal Statistical Society)
a. x_1 = 70, x_2 = 8.6
b. x_1 = 65, x_2 = 11.0
c. x_1 = 83, x_2 = 17.6
d. x_1 = 87, x_2 = 19.6"
"Constructing and Interpreting a Prediction Interval In Exercises 21-30, construct the indicated prediction interval and interpret the results.
25. Mean Wage Construct a 99% prediction interval for the mean annual wage in Exercise 15 when the percentage of employment in STEM occupations is 13% in the industry."
1. Two variables have a positive linear correlation. Does the dependent variable increase or decrease as the independent variable increases? What if the variables have a negative linear correlation?
