1. The table displays the relationship between the mean temperature and hours of daylight for the last eleven days of September.
Date 20 21 22 23 24 25 26 27 28 29 30
Mean Temperature (Fahrenheit) 70.8 70.4 70 69.6 69.2 68.7 68.3 67.9 67.5 67.1 66.6
Hours of Daylight 12.23 12.18 12.13 12.1 12.05 12 11.95 11.9 11.85 11.8 11.77
a. Make a scatterplot to display the relationship between hours of daylight and mean temperature, placing hours of daylight on the x-axis.
b. Describe the relationship shown in the scatterplot.
c. Calculate the correlation for this relationship.
d. Calculate the least-squares regression line for predicting mean temperature from hours of daylight.
e. Calculate and interpret the residual for the day with 12.13 hours of daylight..
f. Would it be appropriate to predict the hours of daylight for October 10 ?
2 A large statistics class recently took a test that had multiple choice and essay questions on it. The summary statistics below are calculated for two quantitative variables, x and y such that x= score on multiple choice part of test (out of 20 possible) and y= score on essay part of test (out of 10 possible). You may assume that the relationship between x and y is linear.
x=15.5 x=1.4 y=8.2 y=1.5 r=0.85
a. Find the equation of the least-squares regression line for predicting y from x. Show your work.
b. Interpret the slope and y intercept of the regression line. Does the y intercept have any meaning in this context?
c. Interpret the correlation.
d. Predict the essay score for a student who scores 20 points on the multiple choice. Does this seem reasonable?
e. One student did score 20 points on the multiple choice. That student also scored 8 points on the essay part. Calculate and interpret the residual for this student.