Question

Following are chest size and weight data for 6 randomly selected bears. Here, x denotes chest size, in inches, and y denotes weight, in pounds. Use the information to complete parts (a) through (f). x 55 44 46 58 40 54 325 263 275 338 256 320 a. Find the regression equation for the data points. y= (Round to two decimal places as needed.) b. Graph the regression equation and the data points OA. 500 500 5007 Weight Weight Weight ща Chest Size Chest Size Chest Size Chest Size c. Describe the apparent relationship between the two variables O A. Weight tends to decrease as chest size increases. OB. Weight tends to increase as chest size increases O C. Weight remains constant as chest size increases. O D. There is no apparent relationship between weight and chest size. d. Identify the predictor and response variables. O A. The predictor variable is bear and the response variable is chest size. OB. The predictor variable is bear and the response variables are weight and chest size. O C. The predictor variable is chest size and the response variable is weight. O D. The predictor variable is weight and the response variable is chest size. e. Identify outliers and potential influential observations. O A. There are no outliers and one influential observation. OB. There are one or more outliers and influential observations O C. There is one outlier and no influential observations. OD. There are no outliers and no influential observations. f. Predict the value of the response variable for a 50-inch chest size. y= pounds (Round to the nearest integer as needed.) Click to select your answer(s)

Answer 1

	X	Y	X * Y	X2	Y2
	55	325	17875	3025	105625
	44	263	11572	1936	69169
	46	275	12650	2116	75625
	58	338	19604	3364	114244
	40	256	10240	1600	65536
	54	320	17280	2916	102400
Total	297	1777	89221	14957	532599

Part a)

Equation of regression line is Ŷ = a + bX
$b = ( n \Sigma XY - \Sigma X \Sigma Y) / ( n\Sigma X^{2} - (\Sigma X)^{2})$
b = ( 6 * 89221 - 297 * 1777 ) / ( 6 * 14957 - ( 297 )²)
b = 4.93

a =( Σ Y - ( b * Σ X) ) / n
a =( 1777 - ( 4.9295 * 297 ) ) / 6
a = 52.15

Equation of regression line becomes Ŷ = 52.15 + 4.93 X

Part b)

Scatter PLot 400 350 300 250 200 150 100 50 0 35 50 55 60 45 40

OD 500 30 Chest Se உ

Part c)

Looking at the graph we can say that there is strong and positive correlation between variables.

OB. Weight tends t inrease as est sie ineases

Part d)

Part e)

OD. There are no outiers and noinfuental obseations

Part f)

When X = 50
Ŷ = 52.154 + 4.93 X
Ŷ = 52.154 + ( 4.93 * 50 )
Ŷ = 299