Linear Regression Analysis
Verbal and / or Numerical Hypotheses Statements
Step 1: State the Hypothesis
Research question: Predict how much more is the selling price, on average, per extra square foot?
Using a two-tailed test for significance at α = .05 the hypothesis are
Ho: p = 0 H1: p ≠ 0
Step 2: Calculate the critical value for a two tailed test using v=n-2 = 105-2 = 103 degrees
We then calculate the critical value for a two tailed test α = .05 with v= 105-2 = 103 degrees of freedom. t .05 df 103 = 1.983
Then we calculate the critical value for r.05
r.05 = t.05/√t.05² + n-2 = 1.983/√1.983² + 103 = 0.192
The critical value of r is ±0.192
Using Excel’s function = CORREL(array1,array2) we get r = 0.371042
t = r√n-2/1-R2 t = 0.371 √105-2 / 1- 0.138 t= 4.055
Step 4: Make the decision
We reject the hypothesis of zero correlation based on these results. In fact there is a high correlation between the home price and the square footage.
We can reject Ho: p=0 since t = 4.055 > t.05 = 1.983.
Regression Analysis Result
Research question: How much more is the selling price on average, per extra square ft.?
The first thing we want to do in our analysis of bivariate data is to create a scatter plot to visually see the relationship between the selling price and the square feet of a home.
We are given the bivariate regression line y=1.959x + 1,790.746 R² = 0.138
We know that the range is -1 ≤ r ≤ 1 and that when r is near zero there is little or no linear relationship between selling price and square foot. In addition we know that when r is near +1 this will indicate that there is a strong positive relationship between them and the closer r is to -1 that a strong negative relationship exists.
We conclude with this test that r = 0.371 indicates that there is a weak positive relationship.
Next we run the Regression Analysis using MegaStats