7.24

  1. The relationship looks fairly linear.
  2. Carbs is the response. Calories is the explanatory.
  3. To predict carbs for items in which only calories are known.
  4. Yes, the relationship looks linear and the residuals are approximately gaussian. (There appears to be a touch of heteroscedasticity in the residual plot, but it isnโ€™t egregious.)

7.26

  1. cm_height = 106 + 0.61 * cm_shoulder_girth
  2. slope: height increases by 0.61 cm for every cm increase in shoulder girth intercept: shoulder girth of 0 cm would correspond to a height of 106 cm (not realistic but just an indication of where it crosses the y-axis)
  3. R2 is 0.45 which means 45% of the variance in height is described by the regression line
  4. 167
  5. The residual is -7, meaning the actual data point is 7 cm less than what the regression predicted
  6. No, 56 cm is way out of range (z-score of -4.9 and not near any of the observed data)

7.30

  1. g_heart_weight = -0.357 + 4.034 * kg_body_weight
  2. 0 kg of body weight would be -0.357 g of heart weight (not realistic but just the y-axis point)
  3. heart weight increases by 4.034 grams for every kilogram increase in body weight
  4. 64.66% of the variance in heart weight is described by the regression line
  5. r = 0.8

7.40

  1. 0.13
  2. Yes, if the true slope were 0 then the observed slope would have a t-score of 4.13, which is very unlikely by chance alone
  3. Yes, the requirements of linearity, nearly normal residuals, constant variability, and independent observations are satisfied.