Question

Use the given data to find the equation of the regression ine. Examine the scatterplot and identity a characteristic of the data that is ignored by the regression ine. 10 8 13 10 12 13 5 4 11 8 6 y 7.44 6.64 12.51 6.86 7.57 8.69 6.19 5.14 8.5 6.63 5.7 Create a soutterplot of the data. Choose the correct graph below. OA ов. Oc. OD. 25+ 20 a 20 151 10 15 10 15 10 10 G G 0 6 8 10 15 20 25 10 15 20 25 05 10 15 20 25 8 10 15 20 25 Find the equation of the regression line (Round the constant two decimal places as needed. Round the coefficient to three decimal places as needed) Identity a characteristic of the data that is ignored by the regression line O A There is no trend in the data OB. There is no characteristic of the data that is ignored by the regression line OC. The data has a pattern that is not a straight line OD. There is an influential point that strongly affects the graph of the regression line

Answer 1

1.

if we plot the scatter plot of Y on X in excel then we will get similar graph to that in option (C) hence

option (C) is correct

2.

let equation is

y=a+bx

from the data we have

$n=11,\sum x*y=797.41,\sum x^2=1008,\bar{x}=9.091,\bar{y}=7.461$

now b can calculated by

$\hat{b}=\frac{\sum xy -n*\bar{x}*\bar{y}}{\sum x^2-n*\bar{x}^2}=\frac{797.41-11*9.091*7.461}{1008-11*9.091^2}=\frac{51.302}{98.891}=0.519$

a = y - *ī= 7.461 – 0.519 * 9.091 = 2.74

so equation is

y=2.74+0.519x

3.

there is a point in the graph that is outside the trend and influenting the graph

hence

option (D) is correct