7.24
(a) There is a positive, moderate strong, linear assosciation between the 
calories and carbs.
(b) Explanatory: calories. Response: carbs(grams)
(c) We can predict carbs in grams for given calorie on a food item. This will
be helpul for customers to get an estimate on the carb content in their food.
(d) Linearity: The plot shows linear trend.
Nearly normal residuals: fairly normal residual plot
Constant variability: fairly constant variability
Independent observations: Not specified.

7.26
(a)

(b1 <- (9.41 * 0.67) / 10.37) 

## [1] 0.6079749

height = 105.9651 + .608 * (shoulder_girth)

(b) b1: For each additional girth in centimeters, the model predicts and additional
0.608 centimeters in height.
b0: When the girth is 0 cm, height is expected to be 105.96 cm. It does not make 
sense to have a girth of 0 cm in this context. Here, the y-intercept
serves only to adjust the height of the line and is meaningless by itself.

(c)

R <- 0.67
R^2

## [1] 0.4489

About 44.89% of the variability in height is accounted by the model ie. explained
by the girth in cm.

(d)

105.9651 + .608 * 100

## [1] 166.7651

(e) A negative residual mean, model over estimated the height.

 (residual = 160 - 166.7651) 

## [1] -6.7651

(f) No, this calculation would require extrapolation.

7.30

(a) Heart_weight = -0.357 + 4.034 * Body_weight 

(b) When body weight = 0, expected heart weight is -0.357. This is obviously not 
    a meaningful value, it just serves to adjust the height of the regression line.

(c) For each additional kg increase in body weight, we expect heart weight in grams 
    to be higher on average by 4.034.

(d) Body weight explains 64.66% of the variability in heart weight.

(e)

(R <- sqrt(0.6466))

## [1] 0.8041144

7.40
(a) y = b0 + b1*x
    b1 = (y - b0) / x

(3.9983 - 4.010) / -0.0883

## [1] 0.1325028

(b) H0: slope is 0 HA: slope is positive
since p value is very small, we need to reject H0 in favour of HA ie. apperance
of the professor has impact on his teaching evaluation score.

(c) Linearity - Follows a fairly linear trend.
    Nearly normal residuals - Slightly left skewed, but still follows normal model.
    Constant Variability - Residuals are randomly scattered around 0. So the 
                           variability is fairly constant.
    Independent observations - Observations are independent.
    
    The conditionis for the least square line ie linear regression is satisfied.