Question

1) Draw a scatter plot for the following data. State if it has a positive, negative, or no correlation. Find the correlation coefficient. Find the equation of the regression line, the coefficient of determination, and the standard error of estimate.

Total
Square
Footage of House
5.0
5.1
5.5
5.8
6.0
Sales
898
980
1105
1277
1433

Answer 1

The equation of the regression line is y = 497.94x - 1590.12 and the coefficient of determination is 0.976

Finding the equation of the regression line

From the question, we have the following parameters that can be used in our computation:

Total Square Footage of House 5.0 5.1 5.5 5.8 6.0

Sales 898 980 1105 1277 1433

Using a graphing tool, we have the following summary

• Sum of X = 27.4
• Sum of Y = 5693
• Mean X = 5.48
• Mean Y = 1138.6
• Sum of squares (SSX) = 0.748
• Sum of products (SP) = 372.46
• Correlation coefficient, r = 0.988

The regression equation is represented as

y = bx + a

Where

b = SP/SSX = 372.46/0.75 = 497.94118

a = MY - bMX = 1138.6 - (497.94*5.48) = -1590.11765

So, we have

y = 497.94x - 1590.12

The coefficient of determination is calculated as

r² = r²

So, we have

r² = 0.988²

Evaluate

r² = 0.976

Hence, the coefficient of determination is 0.976