A California college student wanted to see if there is a relationship between the weather and the color of clothes students wear. He collected data for 13 days in April on these two variables:

X: Weather, ranging from 1 (precipitation) to 6 (bright sunny day).

Y: Clothing brightness, ranging from 1 (black) to 6 (white). Each value of X was recorded right before the start of a philosophy class; Y was the average brightness value for the approximately 20 students who attended the class.

He then used least squares to estimate the following equation: Y = 2.270 + 0.423X.

The standard error of the estimated slope was 0.092 and the value of R² was 0.657.

a. Explain why you either agree or disagree with this student’s decision to let X be weather and Y be clothing, rather than the other way around.

b. Do his regression results indicate that students tend to wear brighter or darker clothing on sunny days?

c. Is the relationship statistically significant at the 5 percent level? How can you tell?

d. What problems do you see with this study?