What is the value of Xbar? 197 187 191 201 211 What is the sample variance of X?

Question

What is the value of Xbar?

  

197

   

187

   

191

   

201

   

211

What is the sample variance of X?

  

681

   

688

   

694

   

665

   

654

What is the sample standard deviation of Xbar?

  

5.46

   

5.35

   

5.30

   

5.41

   

5.68

What is the p-value for a hypothesis test that x=197?

  

.05

   

.07

   

.12

   

.03

   

.10

  

.022

   

.018

   

.024

   

.027

   

.030

  

2.81

   

2.35

   

3.35

   

3.03

   

2.60

  

.224

   

.252

   

.219

   

.211

   

.236

What is the value of SSE (Sum of Square Errors)?

  

28.04

   

25.54

   

26.43

   

26.86

   

27.93

What is the value of the variance of the sample regression Se2? (Hint: What is the regression d.f.?)

  

1.34

   

1.47

   

1.04

   

1.55

   

1.16

  

.0076

   

.0122

   

.0086

   

.0091

   

.0045

  

2.45

   

2.37

   

2.15

   

2.20

   

2.53

If you were to do a two-sided t-test, what are the critical t-values for =.02?

  

±2.500

   

±2.818

   

±2.508

   

±2.069

   

±2.074

Based on the above regression of this data, what is the unbiased estimator of Y when X is 225?

  

8.91

   

9.66

   

9.33

   

8.37

   

8.45

  

.02

   

50

   

1

   

200

   

.50

Suppose, instead of X, a regression was performed on the explanatory variable Z=0.2*X. The new value of R2 would be ____ times as large as the original.

  

200

   

.02

   

1

   

.20

   

20

Please exolain and show work, I really don't understand this

Y X Y-Ybar X-Xbar (Y-Ybar)^2 (X-Xbar)^2 (X-Xbar)(Y-Ybar) xxxxx 164.66667 xxxxx -22.2 0.103 494 xxxxx xxxxx 205.66667 xxxxx 18.8 0.078 353 xxxxx xxxxx 181.33333 xxxxx -5.6 0.271 31 xxxxx xxxxx 184.66667 xxxxx -2.2 0.848 5 xxxxx xxxxx 169 xxxxx -17.9 6.355 320 xxxxx xxxxx 190.33333 xxxxx 3.4 0.520 12 xxxxx xxxxx 241.66667 xxxxx 54.8 5.195 3001 xxxxx xxxxx 191 xxxxx 4.1 0.271 17 xxxxx xxxxx 147.33333 xxxxx -39.6 1.490 1565 xxxxx xxxxx 225.66667 xxxxx 38.8 2.820 1504 xxxxx xxxxx 209.66667 xxxxx 22.8 0.015 519 xxxxx xxxxx 124.66667 xxxxx -62.2 0.461 3872 xxxxx xxxxx 171.66667 xxxxx -15.2 0.773 232 xxxxx xxxxx 195 xxxxx 8.1 2.820 66 xxxxx xxxxx 165.33333 xxxxx -21.6 1.636 465 xxxxx xxxxx 216.33333 xxxxx 29.4 0.230 867 xxxxx xxxxx 203.33333 xxxxx 16.4 0.773 270 xxxxx xxxxx 177.33333 xxxxx -9.6 0.103 91 xxxxx xxxxx 178.66667 xxxxx -8.2 3.690 68 xxxxx xxxxx 176 xxxxx -10.9 0.006 119 xxxxx xxxxx 217 xxxxx 30.1 0.230 907 xxxxx xxxxx 194 xxxxx 7.1 0.006 51 xxxxx xxxxx 157.33333 xxxxx -29.6 4.498 874 xxxxx xxxxx 197.66667 xxxxx 10.8 0.230 116 xxxxx 180.5 4485.333 33.42 15814.37 353.09

Explanation / Answer

#1.
Xbar = (sum of X)/n = 4485.333/24 = 186.888

Hence Xbar = 187

#2.
Variance = 15814.37/(24-1) = 687.58

Variance = 688

#3.
std. dev. = sqrt(variance) = sqrt(688) = 26.22

std. dev. of Xbar = 26.22/sqrt(24) = 5.35

#4.
Test statitics, t = (187 - 197)/5.35 = -1.8692

p-value = 0.07 (This is two tailed test and value is looked up from t-table for df = 23)

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