91Ó°ÊÓ

The given data is

From the given data the graph is

The reason for the curve is that the points are not on a straight line.

The scatter plot slope is sloping upwards, hence the direction is positive.

The reason for this is that all of the points are fairly close together in the same pattern.

The given data is

The graph is

The model with the most linear pattern in the associated scatter plot is the model for the relationship between the variables." Power Model

The given data is

The logarithm of length is $X$, and the logarithm of heart weight is $Y$.

Find the values using the table

$$\begin{gathered} a=\frac{∑y·∑x^2-∑x∑xy}{n∑x^2-{\left(∑x\right)}^2} \\ a=-0.314 \end{gathered}$$

$$\begin{gathered} b=\frac{n∑xy-∑x·∑y}{n∑x^2-{\left(∑x\right)}^2} \\ b=3.139 \end{gathered}$$

then the value of y is

$y=a+b.x$

$y=-0.314+3.139x$

The least-square regression equation is

$\ln y=-0.314+3.139\ln x$.

The given data is

From part (c)

$\ln y=-0.314+3.139\ln x$

Putting the value of x

$\ln y=-0.314+3.139\ln (6.8)$

$=5.7032$

Therefore taking the exponential

$$\begin{gathered} y=e^{\ln y} \\ y=e^{5.7032} \end{gathered}$$

$=299.825$

The expected heart weight is$299.825gms$