Question

2 multiple choice 1.25 points the statistics shown below are of the final exam scores of 10 randomly selected students from a statistics class and the number of hours they studied for the exam. let the number of hours studied be the explanatory variable, x, and final exam score be the response variable, y. \\(\bar{x}=3.5\\), \\(s_x=1.4\\), \\(\bar{y}=72.5\\), \\(s_y=8.2\\), \\(r=0.924\\) find the least-squares regression equation between hours studied and final exam score. \\(\hat{y}=0.158x - 7.955\\) \\(\hat{y}=0.158x + 71.947\\) \\(\hat{y}=5.412x + 91.442\\) \\(\hat{y}=5.412x + 53.558\\)

Explanation:

Step1: Calculate slope (b)

Slope formula: $b = r \cdot \frac{s_y}{s_x}$
$b = 0.924 \cdot \frac{8.2}{1.4} \approx 0.924 \cdot 5.857 \approx 5.412$

Step2: Calculate intercept (a)

Intercept formula: $a = \bar{y} - b\bar{x}$
$a = 72.5 - 5.412 \cdot 3.5 \approx 72.5 - 18.942 = 53.558$

Step3: Form regression equation

Equation: $\hat{y} = bx + a$
$\hat{y} = 5.412x + 53.558$

Answer:

D. $\hat{y}=5.412x + 53.558$