Physical health affects every aspect of one's life, including one's emotional well-being. This study explores the degree to which physical health rating significantly predicts depression, as measured by the Beck Depression Inventory, where scores range from 0-63. Scores 30 and above indicate severe depression. Physical health was rated on a 10-point scale, where 10 is perfect health and 1 is terminally ill. Use SPSS or StatCrunch to examine the ability of physical health to predict depression. Test at a = 0.05.
Step 1: Develop Hypotheses:
a. Independent Variable = Scale: Quantitative (1.5 pts)
b. Dependent Variable = Scale: Quantitative (1.5 pts)
c. Alternative hypothesis in sentence form (1 pt).
d. Null hypothesis in sentence form (1 pt).
e. Write the alternative and null hypotheses using correct notation (2 pts).
H1: The physical health rating significantly predicts depression.
H0: The physical health rating does not significantly predict depression.
Step 2: Establish significance criteria (0.05 pt)
Step 3: Calculate test statistic, R2, and regression equation
g. F = Level of significance (p) = (1 pt)
h. Decision: reject null or fail to reject null (1 pt)
i. r = (1 pt)
i. R2 = (1 pt)
j. Regression Equation: (1.5 pts)
k. If Laila reports a physical health score of 8, what is her predicted depression score? (2 pts)
Step 4: Draw conclusion
l. Write your conclusion in sentence form including appropriate results notation
Simple linear regression results:
Dependent Variable: Depression
Independent Variable: Physical Health
Depression = 49.851387 - 5.6149273 Physical Health
Sample size: 19
R (correlation coefficient) = -0.9117494
R-sq = 0.83128696
Estimate of error standard deviation: 5.4765197
Parameter estimates:
Parameter Estimate Std. Err. Alternative DF T-Stat P-value
Intercept 49.851387 4.0426737 ≠0 17 12.331291 <0.0001
Slope -5.6149273 0.61350558 ≠0 17 -9.1522025 <0.0001
Analysis of variance table for regression model:
Source DF SS MS F-stat P-value
Model 1 2512.2367 2512.2367 83.762811 <0.0001
Error 17 509.86856 29.992268
Total 18 3022.1053
Predicted values:
X value Pred. Y s.e.(Pred. y) 95% C.I. for mean 95% P.I. for new
8 4.9319683 1.6474112 (1.4562346, 8.407702) (-7.1339325, 16.997869)