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

Question

Quizplus · Accepted Answer

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.

The Relationship Between the Cost of a Taxi Ride (Y)and cost^\hat{\text { cost} } cost^

The Relationship Between the Cost of a Taxi Ride (Y)and $\hat{\text { cost} }$