Four research participants take a test of manual dexterity (high scores mean better dexterity) and an anxiety test (high sco
Dexterity Score (x) Anxiety Score (y)
1 10
1 8
2 4
4 -2
(a) Scatter Graph:
Scatter and Regression
12
10
8
Anxiety Score
6 y = -3.6667x + 12.333
4 R² = 0.9603
2
0
0 1 2 3 4 5
-2
-4
Dexterity Score
(b) It appears from the scatter diagram that there is a negative correlation between dexterity and anxiety. Higher the dexterit
(c) R = -0.9800 and R^2 = 0.9603
We see that R = -0.98, which is close to -1, indicating a high degree of negative correlation between dexterity and anxiety. R^
(d) Hypothesis Testing:
H0: There is no correlation between the dexterity score and the anxiety score, that is, β = 0
Ha: The dexterity score and anxiety score are correlated, that is, β ≠ 0.
From the Regression output, we see that the p- value for the population slope is 0.02. Since 0.02 < 0.05, we reject H0 and acc
Conclusion: At α = 0.05, there is sufficient evidence to say that the anxiety level experienced by a person is related to the lev
(e) The present study examined if the dexterity and anxiety were significantly correlated in the population. A regression hypo
(f) We have the following possibilities with respect to the variables x and y:
(i) x and y are not correlated - This appears highly improbable because research has shown that people who have confidence
(ii) x and y are directly correlated - This again, is illogical because we would definitely expect a skilled person to be less anxiou
(iii) x and y are inversely correlated - This is the most probable causalty, because more skills a person has, more confident she
an anxiety test (high scores mean more anxiety). The scores are as follows: Person Dexterity Anxiety 1 1 10 2 1 8 3 2 4 4 4 -2 a. Make
nxiety. Higher the dexterity of a person, lower is her anxiety. This is only to be expected because more skills a person has, more confident
dexterity and anxiety. R^2 = 0.9603, which implies that 96.03% of the variation in anxiety can be explained by the variation in dexterity.
.05, we reject H0 and accept Ha
erson is related to the level of dexterity she possesses.
lation. A regression hypothesis test was conducted and on the basis of the results, there is strong reason to conclude that dexterity and a
ple who have confidence in their skills and abilities and less anxiety-prone than those who are not confident.
d person to be less anxious about an assigned task than one who is not skilled.
n has, more confident she is and therefore less prone to being anxious.
1 1 10 2 1 8 3 2 4 4 4 -2 a. Make a scatter diagram of the scores b. Describe in words the general pattern of correlation, if any c. Figur
kills a person has, more confident she is and therefore less prone to being anxious.
ed by the variation in dexterity.
n to conclude that dexterity and anxiety are correlated.
tern of correlation, if any c. Figure the correlation coefficient d. Figure whether the correlation is statistically significant (use the .05 sig
tically significant (use the .05 significance level, two-tailed) e. Explain the logic of what you have done, writing as if you are speaking to
e, writing as if you are speaking to someone who has never heard of correlation (but who does understand the mean, deviation scores,
and the mean, deviation scores, and hypothesis testing) f. Give three logically possible directions of causality, indicating for each direct
ausality, indicating for each direction whether it is a reasonable explanation for the correlation in light of the variables involved (and wh
of the variables involved (and why)
Regression Analysis
r² 0.960 n 4
r -0.980 k 1
Std. Error 1.291 Dep. Var. Anxiety Score (y)
ANOVA table
Source SS df MS F p-value
Regression 80.6667 1 80.6667 48.40 .0200
Residual 3.3333 2 1.6667
Total 84.0000 3
Regression output confidence interval
variables coefficients std. error t (df=2) p-value 95% lower
Intercept 12.3333 1.2360 9.978 .0099 7.0151
Dexterity Score (x) -3.6667 0.5270 -6.957 .0200 -5.9344
Observation Anxiety Score (y) Predicted Residual
1 10.0 8.7 1.3
2 8.0 8.7 -0.7
3 4.0 5.0 -1.0
4 -2.0 -2.3 0.3
confidence interval
95% upper std. coeff.
17.6516 0.000
-1.3990 -0.980