Exercise 30 presents regression output from a model for predicting the heart weight (in g) of cats from their body weight (in kg). The coefficients are estimated using a dataset of 144 domestic cats. The model output is also provided below.
Estimate Std. Error t value Pr(>|t|)
(Intercept)- 0.3570 .692 -0.5150 .607
body wt 4.034 0.250 16.119 0.000
s = 1.452; R2 = 64.66%; R2adj = 64.41%
- What are the hypotheses for evaluating whether body weight is positively associated with heart weight in cats?
- State the conclusion of the hypothesis test from part 1 in context of the data.
- Calculate a 95% confidence interval for the slope of body weight, and interpret it in context of the data.
- Do the results from the hypothesis test and the confidence interval agree?
I believe i know the null hypothesis (that there is no association) and alternative (there exists an association). I also calculated that in 2. we reject null hypothesis because t = 16. and in 3. I calculated it to be 4.034 plus or minus .5, but i am struggling to understand 2,3, and 4 conceptually