Question

1. Please write out the basic (i.e., single-predictor) regression equation.

Y=...

2. If the unstandardized regression coefficient (the slope of y on x) in a basic, single-predictor regression was found to be b_yx=-0.40, what is the interpretation of "b_yx=-0.40"?

3. If the regression constant (the y intercept) in a basic, single-predictor regression was found to be a=0.80, what is the interpretation of "a=0.80"?

Answer 1

Solution:

Part1) the basic (i.e., single-predictor) regression equation:

where a = Intercept and = Slope coefficient

y = dependent ( Response variable)

x = independent ( Explanatory variable)

Part 2) If the unstandardized regression coefficient (the slope of y on x) in a basic, single-predictor regression was found to be b_yx=-0.40, what is the interpretation of "b_yx=-0.40"?

Slope is the amount of change in response variable for unit change in explanatory variable.

Here slope = b_yx=-0.40, which is negative.

Thus for unit increase in explanatory variable X , there is decrease in response variable Y by 0.40 unit.

Part 3) If the regression constant (the y intercept) in a basic, single-predictor regression was found to be a=0.80, what is the interpretation of "a=0.80"?

Y-intercept is the constant value or it is the value of response variable when value of explanatory variable = 0 or explanatory variable is absent.

Thus here Y-intercept = a = 0.80

The value of response variable is a = 0.80 ,when explanatory variable = X = 0 or it is absent.