The eggs of a species of bird have an average diameter of 23 mm and an SD of 0.45 mm. The weights of the chicks that hatch from these eggs have an average of 6 grams and an SD of 0.5 grams. The correlation between the two variables is 0.75 and the scatter diagram is roughly football shaped.
The slope of the regression line for estimating chick weight based on egg diameter is
0.833 inches per gram
0.675 inches per gram
0.833 grams per mm
0.675 grams per mm
The intercept of the regression line for estimating chick weight based on egg diameter is _______________ grams.
0.833 grams per mm
That answer is incorrect.
0.833 inches per gram
They are all wrong.
0.833 grams per mm is correct:
slope=rsd(y)/sd(x)=0.75*0.5/0.45
slope is 0.8333 grams per mm
The intercept of the regression line for estimating chick weight based on egg diameter is
Intercept=mean y - slope *mean x
Intercept = 23 - 0.8333* 6 = 18
To find the slope and intercept of the regression line for estimating chick weight based on egg diameter, we can use the formula:
\[ \text{slope} = r \frac{{\text{SD of chicks' weight}}}{{\text{SD of egg diameter}}} \]
where \( r \) is the correlation coefficient between the two variables.
Given that the correlation coefficient \( r = 0.75 \), the formula becomes:
\[ \text{slope} = 0.75 \frac{{0.5 \, \text{grams}}}{{0.45 \, \text{mm}}} \]
Simplifying the expression:
\[ \text{slope} = 0.75 \times \frac{{0.5 \, \text{grams}}}{{0.45 \, \text{mm}}} = 0.833 \, \text{grams per mm} \]
So, the slope of the regression line for estimating chick weight based on egg diameter is 0.833 grams per mm.
To find the intercept of the regression line, we use the formula:
\[ \text{intercept} = \text{average chicks' weight} - \text{slope} \times \text{average egg diameter} \]
Given that the average chicks' weight is 6 grams and the average egg diameter is 23 mm, the formula becomes:
\[ \text{intercept} = 6 \, \text{grams} - 0.833 \, \text{grams per mm} \times 23 \, \text{mm} \]
Simplifying the expression:
\[ \text{intercept} = 6 - 19.159 = -13.159 \, \text{grams} \]
So, the intercept of the regression line for estimating chick weight based on egg diameter is -13.159 grams.
In summary, the slope of the regression line for estimating chick weight based on egg diameter is 0.833 grams per mm and the intercept is -13.159 grams.