Data from a study investigating the relationship between roadway surface temperature (x) and pavement deflection (y) can be summarized as follows:

20 measurements taken

P i yi = 12.75 and P i y 2 i = 8.86

P i xi = 1478 and P i x 2 i = 143215.8

P i xiyi = 1083.67

a) If the Gaussian distribution is used to model the roadway temperature, what is the probability that a new measurement would be greater than 79F?

b) Derive the linear regression equation that relates the roadway temperature with the pavement deflection.

c) Predict what pavement deflection would be observed if the roadway temperature was 85F.

d) What is the 95% confidence interval for the prediction at 85F if the total cumulative squared error of the regression is 0.26?

Data from a study investigating the relationship between roadway surface temperature (1) and pavement deflection (y) can be summarized as follows: . 20 measurements taken Diy = 12.75 and y = 8.86 ..x = 1478 and 1=143215.8 ..y = 1083.67 a) If the Gaussian distribution is used to model the roadway temperature, what is the probability that a new measurement would be greater than 79F? b) Derive the linear regression equation that relates the roadway temper- ature with the pavement deflection. c) Predict what pavement deflection would be observed if the roadway temperature was 85F d) What is the 95% confidence interval for the prediction at 85F if the total cumulative squared error of the regression is 0.26? Data from a study investigating the relationship between roadway surface temperature (1) and pavement deflection (y) can be summarized as follows: . 20 measurements taken Diy = 12.75 and y = 8.86 ..x = 1478 and 1=143215.8 ..y = 1083.67 a) If the Gaussian distribution is used to model the roadway temperature, what is the probability that a new measurement would be greater than 79F? b) Derive the linear regression equation that relates the roadway temper- ature with the pavement deflection. c) Predict what pavement deflection would be observed if the roadway temperature was 85F d) What is the 95% confidence interval for the prediction at 85F if the total cumulative squared error of the regression is 0.26