Question

not ho chi The data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best predicted weight of a bear with a chest size of 48 inches. Is the result close to the actual weight of 218 pounds? Use a significance level of 0.05. Chest size (inches) 58 49 58 43 46 57 Weight (pounds) 355 266 332 177 246 348 Click the icon to view the critical values of the Pearson correlation coefficient r. What is the regression equation? = 0x (Round to one decimal place as needed.) What is the best predicted weight of a bear with a chest size of 48 inches? The best predicted weight for a bear with a chest size of 48 inches is pounds. (Round to one decimal place as needed.) Is the result close to the actual weight of 218 pounds? a h O A. This result is exactly the same as the actual weight of the bear OB. This result is not very close to the actual weight of the bear. OC. This result is close to the actual weight of the bear OD. This result is very close to the actual weight of the bear U vo ca

Answer 1

Ans 1) Linear regression equation: ans,

y = -243.6 + 10.2.c

Ans 2) put x = 48 in equation : pounds ans.

y -243.6 + 10.2 x 48 = 246.0

Ans b) The result is not very close to the actual weight of the bear.

Explanation: 246 $\neq$ 218

Explanation:

Linear regression Coefficient:

$b = \frac{\sum_{i=1}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sum_{i=1}^{n}(x_{i}-\bar{x})^2}$

and

a=y-b.c

Mean =

58 +19+ 6 +57 = 51.83

Mean = $\bar{y} = \frac{355+266+...+348}{6} = 287.33$

$\sum_{i=1}^{6}(x_{i}-\bar{x})(y_{i}-\bar{y}) = (417.28+60.44+...+313.44) = 2282.33$

$\sum_{i=1}^{6}(x_{i}-\bar{x})^2 = (38.028+8.028+...+26.69) = 222.83$

therefore,

$b = \frac{2282.33}{222.83} = 10.2$

$a = 287.3 - 10.2\times 51.83 = -243.6$

X-X Chest size (x) 58 Weight (y) 355 266 332 49 58 6.166666667 -2.833333333 6.166666667 -8.833333333 -5.833333333 5.166666667 y- (x-x)? (y-7) (x-x)(y-7) 67.66667 38.02778 4578.77778 417.2778 -21.3333 8.027778 455.111111 60.44444 44.66667 38.02778 1995.11111 275.4444 -110.333 78.02778 12173.4444 974.6111 -41.3333 34.02778 1708.44444 241.1111 60.66667 26.69444 3680.44444 313.4444 43 177 46 246 57 348 Mean (*) Mean (y) = Sum(x-7)(y-7) = Sum(x-x)2 = Sum(y-7)+= 51.83333333 287.3333333 2282.333333 222.8333333 24591.33333