Obesity is a growing problem around the world. Surprisingly, some people don't gain weight even when they overeat. Perhaps fidgeting and other "nonexercise activity" (NEA) explains why—some people may spontaneously increase nonexercise activity when fed more. Researchers deliberately overfed 16 healthy randomly selected young adults who agreed to participate in the study for 8 weeks. They measured fat gain (in kilograms, kg) and, as an explanatory variable, change in energy use (in kilocalories, or Calories, Cal) from activity other than deliberate exercise—fidgeting, daily living, and the like.
Here is part of the Minitab output for regressing fat gain on NEA change in this study, along with a prediction for a person adding 400 NEA calories:

Predictor Coef SE Coef T P
Constant 3.5051 0.3036 11.54 0.000
NEA change −0.0034415 0.0007414 −4.64 0.000

S = 0.739853 R-Sq = 60.6% R-Sq(adj) = 57.8%
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 2.129 0.193 (1.714, 2.543) (0.488, 3.769)

(a) What is the regression standard error for these data?

a) 0.00070 b) 0.3036 c) 0.7399

(b) Confidence intervals and tests for these data use the t distribution with what degrees of freedom?