91影视

The given data provides the information of the shoe print (in cm) and the height (in cm), as follows.

The formula for the estimated regression line is

\(y = {b_0} + {b_1}x\).

Here,

\({b_0}\)is the Y-intercept,

\({b_1}\)is the slope,

\(x\)is the explanatory variable, and

\(\hat y\)is the response variable (predicted value).

Let X denote the foot length (in cm) and Y denote the height (in cm) of the male.

The calculations required to compute the slope and intercept are as follows.

The sample size is \(\left( n \right) = 5\).

The slope is computed as

\(\begin{array}{c}{b_1} = \frac{{n\left( {\sum {xy} } \right) - \left( {\sum x } \right)\left( {\sum y } \right)}}{{n\left( {\sum {{x^2}} } \right) - {{\left( {\sum x } \right)}^2}}}\\ = \frac{{5 \times 23209.27 - 130.8 \times 886.5}}{{5 \times 3426.96 - {{130.8}^2}}}\\ = 3.5226\end{array}\).

The intercept is computed as

\(\begin{array}{c}{b_0} = \frac{{\left( {\sum y } \right)\left( {\sum {{x^2}} } \right) - \left( {\sum x } \right)\left( {\sum {xy} } \right)}}{{n\left( {\sum {{x^2}} } \right) - {{\left( {\sum x } \right)}^2}}}\\ = \frac{{886.5 \times 3426.96 - 130.8 \times 23209.27}}{{5 \times 3426.96 - {{130.8}^2}}}\\ = 85.15\end{array}\).

The estimated regression equation is

\(\begin{array}{c}\hat y = {b_0} + {b_1}x\\ = 85.15 + 3.5226x\end{array}\).

Refer to exercise 18 of section 10-1 for the following result.

1) The scatter plot does not show an approximate linear relationship between the variables.

2) The P-value is 0.085.

As the P-value is greater than the level of significance (0.05), the null hypothesis is failed to be rejected.

Therefore, the correlation is not significant.

Referring to figure 10-5, the criteria for a good regression model are not satisfied.

The best-predicted value of a variable is simply its sample mean.

The best-predicted height of a male who has a foot length of 28 cm is obtained as the mean of the sample responses.

The sample mean is computed as

\(\begin{array}{c}\bar y = \frac{{\sum\limits_{i = }^n {{y_i}} }}{n}\\ = \frac{{\left( {175.3 + 177.8 + ... + 172.7} \right)}}{5}\\ = 177.3\end{array}\).

Therefore, the best-predicted height of the male who has a foot length of 28 cm will be 177 cm. As the best-predicted value is the mean height (177 cm), it will not help the police to describe the male.