Regression methods were used to analyze the data from a study investigating the relationship between roadway surface temperature (x), in °F, and pavement deflection (y). Summary quantities were:
n = 20
?yi =12.75
?xi = 1478
Sxx = 3399.16
Sxy = 141.445
Syy = 7.31875
a) Estimate the degree of linear correlation among surface temperature and pavement deflection. Explain this quantity
b) At 5% level of significance, test that the higher the surface temperature, the larger the pavement deflection. How does your conclusion match with that in part (a)?
c) Find the estimated regression line. What are your assumptions?
d) What change in mean pavement deflection would be expected for a 1°F change in surface temperature?
e) Estimate the error variance.
f) Predict which pavement deflection would be observed when the surface temperature is 90°F, using a 95% interval.
g) Calculate the coefficient of determination and interpret it.