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 76 225
Player_2 75 195
Player_3 72 180
Player_4 82 231
Player_5 69 185
Player_6 74 190
Player_7 75 228
Player_8 71 200
Player_9 75 230

(b) Determine the​ least-squares regression line. Test whether there is a linear relation between height and weight at the α=0.05 level of significance.

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

A.^y =4.1174.117x−98.9

B.^y= −98.9x+4.117

C.^y=4.117x−100.9

D.^y =8.117x−98.9

Test whether there is a linear relation between height and weight at the α=0.05 level of significance.

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

A .H0​:β0=0

H1​:β0≠0

B. H0​: β1=0

H1​:β1>0

C. H0​:β0=0

H1​:β0>0

D. H0​: β1=0

H1​:β1≠0

Determine the​ P-value for this hypothesis test.

​P-value=_____ ​(Round to three decimal places as​ needed.)

State the appropriate conclusion at the α=0.05 level of significance. Choose the correct answer below.

A.Reject H0. There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

B.Do not reject H0. There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

C.Reject H0. There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

D.Do not reject H0. There is not 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-value=_____ ​(Round to three decimal places as​ needed.)

State the appropriate conclusion at the α=0.05 level of significance. Choose the correct answer below.

A.Do not reject H0. There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

B.Reject H0. There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

C.Do not reject H0. There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

D.Reject H0. There is 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?

A.No

B.Yes

Answer 1

Regression equation is

A.^y =4.117x − 98.9

D) Ho :- beta1 = 0. Vs. beta1 not equal to 0

t statistics = 2.7186

P value = 0.030

P value = 0.030 < 0.05 = alpha

C.Reject H0. There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

Remove player 4

Regression equation is

Y ^ = - 214.0030 + 5.6985 x

T stat = 2.2847

P value = 0.06240 > 0.05 = alpha

Fail to reject Ho

C.Do not reject H0. There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

Yes , player 4 is influential.