1. An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 20 metal sheets are given below. Use the simple linear regression model. 

∑X = 40
∑X² = 200
∑Y = 70
∑Y² = 545
∑XY = 320

Find the estimated y intercept and slope and write the equation of the least squares regression line. Estimate Y when X is equal to 3 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation.

2. Use the following results obtained from a simple linear regression analysis with 15 observations.

YHat= 35.5- (1.25)X
R²= 0.8745 and  s_b1 =  0.50

Interpret regression results and the value of the coefficient of Determination. Predict the value of Y when X is equal to 10. Calculate the correlation coefficient between Y and X. Test to determine if there is a significant relationship between the independent and dependent variable at a = 0.05. Perform a two-tailed test.