In a newspaper article written in the Chicago Tribune, it was claimed that poorer school districts have shorter school days.

(a) The least-squares regression line between length, y, and income, x, is ŷ = -0.0102 x + 7.11. Interpret the slope of this regression line. Does it make sense to interpret the y-intercept? If so, interpret the y-intercept.
(b) Predict the length of the school day for a district in which 20% of the population is low income by letting x = 20.
(c) Based on the following residual plot, do you think a linear model is appropriate for describing the relation between length of school day and income? Why?

(d) Included in the output from Minitab was a notification that three observations were influential. Based on the scatter diagram in part (a), which three observations do you think might be influential?
(e) This same article included average Prairie State Achievement Examination (PSAE) scores for each district. The article implied that shorter school days result in lower PSAE scores. The correlation between PSAE score and length of school day is 0.517. A scatter diagram treating PSAE as the response variable is shown next. Do you believe that a longer school day is positively associated with a higher PSAE score?

(f) The correlation between percentage of the population that is low income and PSAE score is -0.720. A scatter diagram treating PSAE score as the response variable is shown next. Do you believe that percentage of the population that is low income is negatively associated with PSAE score?

Transcribed Image Text:

Length vs. Income 7.6 7.4 - 7.2 A 7.0 6.8 - 6.6 - 6.4 - 6.2 - 6.0 10 20 30 40 50 60 70 80 0 90 Percent Low Income Length of School Day (hours) Residuals vs. Income 0.50 0.25 0.00 -0.25 -0.50 -0.75 10 20 30 40 50 60 70 80 90 Percent Low Income Residual