Question

The data in the accompanying table represent the heights and weights of a random sample of professional baseball players. Complete parts ​(a) through ​(c) below.

Player	Height​ (inches)	Weight​ (pounds)
Player 1	75	225
Player 2	75	197
Player 3	72	180
Player 4	82	231
Player 5	69	185
Player 6	7474	190190
Player 7	75	228
Player 8	71	200
Player 9	75	230

(a) Draw a scatter diagram of the​ data, treating height as the explanatory variable and weight as the response variable. Choose the correct graph below.

​(b) Determine the​ least-squares regression line. Test whether there is a linear relation between height and weight at the

alphaαequals=0.05

level of significance.

Determine the​ least-squares regression line. Choose the correct answer below.

A.

ModifyingAbove y with caretyequals=8.0588.058xnegative 93.9−93.9

B.

ModifyingAbove y with caretyequals=negative 93.9−93.9xplus+4.0584.058

C.

ModifyingAbove y with caretyequals=4.0584.058xnegative 93.9−93.9

D.

ModifyingAbove y with caretyequals=4.0584.058xnegative 95.9

Test whether there is a linear relation between height and weight at the

alphaαequals=0.05

level of significance.

State the null and alternative hypotheses. Choose the correct answer below.

A.

Upper H 0H0​:

beta 0β0equals=0

Upper H 1H1​:

beta 0β0not equals≠0

B.

Upper H 0H0​:

beta 1β1equals=0

Upper H 1H1​:

beta 1β1greater than>0

C.

Upper H 0H0​:

beta 1β1equals=0

Upper H 1H1​:

beta 1β1not equals≠0

D.

Upper H 0H0​:

beta 0β0equals=0

Upper H 1H1​:

beta 0β0greater than>0

Determine the​ P-value for this hypothesis test.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.) State the appropriate conclusion at the

alphaαequals=0.05

level of significance. Choose the correct answer below.

A.Reject

Upper H 0H0.

There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

B.Do not reject

Upper H 0H0.

There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

C.Reject

Upper H 0H0.

There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

D.Do not reject

Upper H 0H0.

There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

​(c) Remove the values listed for Player 4 from the data table. Test whether there is a linear relation between height and weight. Do you think that Player 4 is​ influential?

Determine the​ P-value for this hypothesis test.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.) State the appropriate conclusion at the

alphaαequals=0.05

level of significance. Choose the correct answer below.

A.Do not reject

Upper H 0H0.

There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

B.Reject

Upper H 0H0.

There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

C.Do not reject

Upper H 0H0.

There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

D.Reject

Upper H 0H0.

There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

Do you think that Player 4 is​ influential?

No

Yes

Click to select your answer(s).

Answer 1

a)

Scatter plot gives an insight of positive relation between weight and height.

b)

Player	Height​ (inches) xi	Weight​ (pounds) yi	xi^2	yi^2	xi*yi
Player 1	75	225	5625	50625	16875
Player 2	75	197	5625	38809	14775
Player 3	72	180	5184	32400	12960
Player 4	82	231	6724	53361	18942
Player 5	69	185	4761	34225	12765
Player 6	74	190	5476	36100	14060
Player 7	75	228	5625	51984	17100
Player 8	71	200	5041	40000	14200
Player 9	75	230	5625	52900	17250
Sum	668	1866	49686	390404	138927
Average	74.22222	207.3333

S_xx = 105.56

S_yy = 3520

S_xy = 428.33

b₁ = S_xy/ S_xx = 4.058

b₀ = 207.33 - 4.058*74.22 = -93.261

equation => Y = -93.9 + 4.058 X

Test for significance

H₀​:β₁ = 0

H₁​:β₁ ≠ 0

ANOVA
	df	SS	MS	F	Significance F
Regression	1	1738.132	1738.132	6.828182	0.034757
Residual	7	1781.868	254.5526
Total	8	3520

Since p-value (0.034) is less than 0.05 we reject null hypothesis and conclude that there exist a significant linear relationship.

There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

c)

Player	Height​ (inches) xi	Weight​ (pounds) yi	xi^2	yi^2	xi*yi
Player 1	75	225	5625	50625	16875
Player 2	75	197	5625	38809	14775
Player 3	72	180	5184	32400	12960
Player 5	69	185	4761	34225	12765
Player 6	74	190	5476	36100	14060
Player 7	75	228	5625	51984	17100
Player 8	71	200	5041	40000	14200
Player 9	75	230	5625	52900	17250
Sum	586	1635	42962	337043	119985
Average	73.25	204.375

S_xx = 37.5

S_yy = 2889.875

S_xy = 221.25

b₁ = S_xy/ S_xx = 5.9

b₀ = 204.375 - 5.9*73.25 = -227.8

Y = 5.9X - 227.8

Test for significance

ANOVA
	df	SS	MS	F	Significance F
Regression	1	1305.375	1305.375	4.943042	0.067889
Residual	6	1584.5	264.0833
Total	7	2889.875

Since p-value (0.0678) is more than 0.05 we fail to reject null hypothesis and conclude that there doesnot exist a significant linear relationship between the height and weight of baseball players.

Yes Player 4 is an influential player.