Question

Business statistics regression; Below is a histogram for the Ireland returns from the countries dataset. There are n=107 observations for this variable.

1. The sample mean of the Ireland returns is about

(I) -.16  (II) -.051 (III) .012 (IV) .083

2. The sample standard deviation of the Ireland returns is about

(I)0.01 (II) .06 (III) .15 (IV) -.05

Below is a scatterplot of the Ireland returns vs. the UK returns. There are n=107 observations.

3. The sample correlation between the Ireland returns and UK returns is

( I ) .68 (II) -2.3 (III) .17 (IV) .97

4. The sample standard deviation of the UK returns is about

( I ) 0.001 (II) .1 (III) .02 (IV) .05

Suppose we run a regression using these returns with y= Ireland (outcome variable) and x=UK (predictor variable)

SST = SSR + SSE

SSR = S(  )²

SSE = S(y  )²

SST = SS_yy= S(y  )²

SS_xy= S(x  )(y  )

SS_xx= S(x  )²

r =

SS_e =   ,    SSE =(1-R²) = SST (S_e = standard deviation of errors)

S_b=

†=

5. The slope estimate, b. in this regression would be approximately:

( I ) -.3 (II) .25 (III) .8 (IV) 1.3

6. The Intercept estimate, a. in this regression would be approximately:

( I ) .003 (II) -.12 (III) .18 (IV) .09

7. What is the sample standard deviation of errors (S_e) from the regression? (explain)
8. Test at the 10% significance level whether the UK (x) has a linear relationship with the Ireland returns? (explain)

30 25 20 (5 5 LO -0,15 (-15)-(13 |(sat (20) o-(E0-) O-03 03 .06 b0-90 . 09-.12 .12-.15 15-18 > 18 Below is a scatterplot of the Ireland returns vs. the UK returns. There are n = 107 observations 024 0.18 012 0.06 0.00 006 18 O.12 016 004 0.09 0.00 0.04 0.09 012 pueje

Answer 1

a. Since the histogram suggests that the distribution is approximately normal, the mean would lie between 0-0.03.

Hence correct option is (III) 0.012

b. Since, this is normal, standard deviation can be roughly calculated as Range/6.

Hence, the correct option is (II) 0.06

c. Scatter plot shows fairly strong correlation.

Hence, the correct option is (I) 0.68

d. Since, this is also almost normal, standard deviation can be roughly calculated as Range/6.

Hence, the correct option is (III) 0.02