The relationship between the cost of a taxi ride (y) and the length of the ride (x) is analyzed.The mean length was 4.6 km with a standard deviation of 1.1.The mean cost was $8.70 with a standard deviation of 2.0.The correlation between the cost and the length was 0.81.

A) $\widehat{\text{ cost}}$ = 0.336 + 1.82 length
B) $\widehat{\text{ cost}}$ = 1.93 + 1.47 length
C) $\widehat{\text{ cost}}$ = -113 + 26.5 length
D) $\widehat{\text{ cost}}$ = 6.65 + 0.446 length
E) $\widehat{\text{ cost}}$ = -458 + 101 length

The correct choice can be determined using the formula for the slope ( $b$ ) of the regression line: $b=r(\frac{s_y}{s_x})$ , where $r$ is the correlation coefficient, $s_y$ is the standard deviation of the dependent variable (cost), and $s_x$ is the standard deviation of the independent variable (length). The intercept ( $a$ ) can be calculated using the formula $a=\bar{y}-b\bar{x}$ , where $\bar{y}$ is the mean of the dependent variable and $\bar{x}$ is the mean of the independent variable. Given $r=0.81$ , $s_y=2.0$ , $s_x=1.1$ , $\bar{y}=8.70$ , and $\bar{x}=4.6$ , the slope $b$ is approximately 1.47 and the intercept $a$ is approximately 1.93, making option B the correct linear regression equation.