6B

x y
0 100
1 103
2 106
3 109
x y
2 1
0 3
2 5
4 7
Skill or Concept: I can . . . Questions to check your understanding Rating
from 1 to 5
Identify the estimated y-intercept and estimated slope from the equation of the line. 1–3
Interpret the estimated slope in context. 4, 5
Chirps per second Temperature (in oF)
20 88.6
16 71.6
19.8 93.3
18.4 84.3
17.1 80.6
15.5 75.2
14.7 69.7
17.1 82
15.4 69.4
16.2 83.3
15 79.6
17.2 82.6
16 80.6
17 83.5
14.4 76.3

A graph and some tables. The first table is labeled "Descriptive Statistics." The columns are labeled "Variable," "n," "Mean," "Standard Deviation," "Minimum," "Q1," "Median," "Q3," and "Maximum." The first row variable is gas mileage in mpg. For n, its value is 25. For mean, its value is 24.56. For standard deviation, its value is 5.92. For minimum, its value is 17.00. For Q1, its value is 21.00. For median, its value is 23.00. For Q3, its value is 29.00. For maximum, its value is 38.00. The next row variable is weight in hundreds of pounds. For n, its value is 25. For mean, its value is 40.38. For standard deviation, its value is 9.82. For minimum, its value is 24.60. For Q1, the value is 34.17. For median, the value is 38.63. For Q3, the value is 46.12. For maximum, its value is 64.00. Beneath this is a scatterplot with a line of best fit. Its horizontal axis is labeled "weight in hundreds of pounds" and its vertical axis is labeled "gas mileage in miles per gallon." Beneath the scatterplot is another table labeled "Linear Regression Equation." The columns are labeled "parameter" and "estimate." The first row has "intercept" under parameter and 45.65 under estimate. The second row has "Slope (weight in hundreds of pounds)" under parameter and -0.5222 under estimate. A graph showing the relationship between the explanatory variable, which is on the horizontal axis, labeled x, and the response or predicted value, which is on the vertical axis, labeled y. There is a line running through the graph, labeled "b" where it intersects with the y-axis. There are two points along the line. The lower one has a blue arrow pointing up above it. Where this arrow ends, there is a red arrow pointing to the right that ends at the second point. These two arrows and the line segment between the two points form a triangle. Beneath the points, "m = rise over run" is written. Rise is written in blue to correspond to the blue arrow and run is written in red to correspond to the red arrow. A graph showing the relationship between the explanatory variable, which is on the horizontal axis, labeled x, and the response or predicted value, which is on the vertical axis, labeled y. There is a line running through the graph, labeled "a" where it intersects with the y-axis. There are two points along the line. The lower one has a blue arrow pointing up above it. Where this arrow ends, there is a red arrow pointing to the right that ends at the second point. These two arrows and the line segment between the two points form a triangle. Beneath the points, "b = rise over run" is written. Rise is written in blue to correspond to the blue arrow and run is written in red to correspond to the red arrow. An equation that reads y = a + bx. The "y" is labeled as the predicted response or predicted value. The "a" is labeled as the estimated value of the y-intercept when x = 0. The "b" is labeled as the slope of line - constant rate of change. Lastly, the x is labeled as the explanatory variable. A scatterplot of alcohol content versus calories, using data on 227 domestic and international beers as sourced from Beer100.com. The horizontal axis is labeled "Alcohol Content (%)" and the vertical axis is labeled "Calories." The graph also has a labeled line of best fit. Above, it says "Regression Line y = 8.27 + 25.2x" It is also highlighted and labeled as equation of the line of best fit. Beneath the graph, there is a table labeled Linear Regression Equation. It has a column labeled parameter and another labeled estimate. The first row has intercept under parameter and 8.271 under estimate. The second row has scope (alcohol content (%)) under parameter and 28.24 under estimate. There is another table labeled Model Summary. It has a column labeled Statistic and another labeled Value. The first row has correlation coefficient r under statistic and 0.906 under value. This row is also highlighted and labeled correlation coefficient. The next row has coefficient of determination r squared under statistic and 82.0% under value. The last row has residual standard deviation under statistic and 17.44 under value. A scatterplot labeled "Chirps per second" on the x-axis and "Temperature in degrees Fahrenheit." Above the graph, it says "Regression Line: y = 25.2 + 3.29x" The scatterplot has points at approximately (14.5, 76.5), (14.7, 69.5), (15, 79.5), (15.35, 69), (15.5, 75), (16, 72), (16, 81), (16.2, 83), (17, 83), (17.1, 81), (17.1, 82.5), (17.2, 83), (18.4, 84), (19.75, 87.5), (20, 88.5).

Linear Regression Equation:

Parameter Estimate
Intercept 25.23
Slope (Chirps per Second) 3.291

 

Model Summary:

Statistic Value
Correlation Coefficient r 0.835
Coefficient of Determination r^2 69.7%
Residual Standard Deviation 3.829

A right triangle. The vertical edge of the triangle is labeled "Rise," the horizontal edge is labeled "Run," and the diagonal edge is labeled "Slant." Two triangles, labeled T1 and T2, respectively. T1 is labeled 4 on the horizontal side, 3 on the vertical side, and 5 on the diagonal side. T2 is labeled 8 on the horizontal side, 6 on the vertical side, and 10 on the diagonal side. A triangle labeled T3. Its horizontal edge is labeled 12 and its vertical edge is labeled 9. A grid

Glossary

right triangle
a triangle that contains one right angle (90 degrees).
base
the horizontal side of a right triangle.