Please answer all 3 parts and show full work for all of them

Researchers measured the diameters of 22 trees in a central Amazon rain forest. They also used Carbon-dating to determine the age of each tree. After checking all relevant assumptions, they calculated a Pearson correlation coefficient of r= 0.67 for the age of the trees compared to their diameter.

Given: Critical value = 2.086.

a) Calculate the 95% confidence interval for the correlation coefficient for this population of trees.

b) Given your answer to part (a), is there a significant linear relationship between age and diameter for these trees?Why/why not?

c) The researchers find that the trees had a mean age or 17.2 years, with a standard deviation of 4.9 years. The diameters had a mean of 23.3cm, with a standard deviation of 5.3cm. Assuming all relevant assumptions were met, calculate the OLS linear regression equation for predicting tree age based on diameter. Write the full equation, defining any variables used.