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 shoe print (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

\(\begin{array}{c}{b_1} = \frac{{n\left( {\sum {xy} } \right) - \left( {\sum x } \right)\left( {\sum y } \right)}}{{n\left( {\sum {{x^2}} } \right) - {{\left( {\sum x } \right)}^2}}}\\ = \frac{{5 \times 26650 - 150.2 \times 886.5}}{{5 \times 4523.1 - {{150.2}^2}}}\\ = 1.73\end{array}\).

The intercept is computed as

\(\begin{array}{c}{b_0} = \frac{{\left( {\sum y } \right)\left( {\sum {{x^2}} } \right) - \left( {\sum x } \right)\left( {\sum {xy} } \right)}}{{n\left( {\sum {{x^2}} } \right) - {{\left( {\sum x } \right)}^2}}}\\ = \frac{{886.5 \times 4523.1 - 150.2 \times 26650}}{{5 \times 4523.1 - {{150.2}^2}}}\\ = 125.4\end{array}\).

So, the estimated regression equation is

\(\begin{array}{c}\hat y = {b_0} + {b_1}x\\ = 125 + 1.73x\end{array}\).

Refer to exercise 17 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 0.294.

As theP-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 the sample mean of the response variable.

The best-predicted height of a male who has a shoe-print length of 31.3 cm is computed as follows.

The sample mean:

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

Therefore, the best-predicted height of a male who has a shoe-print length of 31.3 cm will be approximately 177 cm.

It will not be helpful to the police in trying to obtain a description of the male because the resultant value is obtained from a bad regression model.