University:
York University
Course:
CHEM 2021 | Introductory Organic Chemistry II
Academic year:

2022
Views:

309

Pages:

2
Author:

Nesbyenvkk

Use the following information for numbers 1 – 4: The table and scatterplot below describe the relationship between latitude and average July temperature in the twelve largest U.S. cities. The equation of the least-squares regression line is yˆ 106.5 0.782 x , where ŷ = July temperature in Fº and x = latitude. 1. Interpret the slope of the least-squares line in the context of the problem. For each 1-degree increase in latitude, the predicted average July temperature decreases by 0.782 degrees. 2. Predict the average July temperature for a city at a latitude of 42 degrees. Show your work. yˆ 106.5 0.782 42  73.66  3. Find the value of the residual for Detroit. Show your work. Interpret the value of the residual in the context of the problem. The observed value for Detroit is 74°, the predicted value for Detroit 73.66° residual = 74 – 73.66 = 0.34 The line under predicts the average July temperature in Detroit by about 0.34°. 4. The value of r2 for these data is 0.277. Interpret this value in the context of the problem. 28% of the variation in average July temperature can be accounted for by the LSRL of average July temperature on latitude. Use the following information for numbers 5 – 7 Alana’s favorite exercise machine is a stair climber. On the “random” setting, it changes speeds at regular intervals, so the total number of simulated “floors” she climbs varies from session to session. She also exercises for different lengths of time each session. She decides to explore the relationship between the number of minutes she works out on the stair climber and the number of floors it tells her that she’s climbed. She records minutes of climbing time and number of floors climbed for six exercise sessions. Computer output and a residual plot from a linear regression analysis of the data are shown below. 5. What is the equation of the least-squares line? Be sure to define any variables you use. Floors climbed = –3.822 + 5.215(number of minutes) 6. Is a line an appropriate model for these data? Justify your answer. Since there is no distinctive pattern in the residuals, the linear model is a good fit. 7. What percentage of the variation in number of floors climbed can be accounted for by this regression? 98.9%