Question

Data Display Row IQ            Score              Mus.Apt. 1                      95                    30 2                      106                  37 3                      110                  35 4                      104                  28 5                      98                    17 6                      114                  45 7                      123                  33 8                      100                  18 9                      98                    24 10                    88                    18 11                    102                  30 12                    105                  30 13                    111                  32 14                    106                  33 15                    110                  38 16                    143                  42 17                    106                  40 18                    98                    20 19                    104                  23 20                    97                    25 Descriptive Statistics Variable           N                      Mean               Median                        TrMean            StDev             SEMean IQ Score          20                    105.90                         104.50                         104.83                         11.60             2.59 Mus.Apt.          20                    29.90               30.00               29.78               8.27                 1.85 Variable           Min                  Max                 Q1                   Q3 IQ Score          88.00               143.00                         98.00               110.00 Mus.Apt.          17.00               45.00               23.25               36.50 Regression Analysis The regression equation is __________ = _________________________________________ Predictor          Coef                 Stdev               t-ratio               p Constant          .22.26              12.94               −1.72               0.102 IQ Score          0.4925            0.1215             ______                       ______ s = 6.143 R-sq = 47.7% R-sq(adj) = 44.8%

A. Which of these is the equation of the regression line?

a. IQ Score = .4925 − 22.26(Mus.Apt.)

b. Mus.Apt. = .4925 − 22.26(IQ Score)

c. Mus.Apt. = −22.26 + .4925(IQ Score)

d. IQ Score = −22.26 + .4925(Mus.Apt.)

e. IQ Score = Constant + .4925x

B. From the printout above, we can determine the test statistic (t) we’d use to test the hypothesis H₀: β₁= 0. Its value is:

a. 4.05.

b. .000743.

c. 6.143.

d. .08.

e. −1.72.

C. Which of these is a 95% confidence interval for the slope of the population regression line?

a. (.147, .838)

b. (.237, .748)

c. (−59.50, 14.98)

d. (−17.19, 18.17)

e. (.143, .842)

Answer 1

(A) Answer is c

From the Regression Analysis Table, coefficient of IQ score is 0.4925 and the constant value is -22.26. Hence the linear regression gives the equation:

Mus.Apt.= -22.26+0.4925(IQ Score)

Therefore option C is correct.

(B) Answer is a

b₁=0.4925 and Standard Error of b₁, SE=0.1215

Hence value of statistic= b₁/SE=0.4925/0.1215=4.05

Therefore, the correct answer is 4.05 (a)

(C) Answer is b

(the degrees of freedom=n-2=20-2=18

The confidence interval for b1 is: (b₁-t_0.025,18*SE, b₁+t_0.025,18*SE)

=(0.4925-2.101*1215, 0.4925+2.101*1215)=(0.237,0.748)

Hence, the answer is B