Question 1206833
the regression equation is y = a + bx.
this equation becomes y = 13.3613 + .04913x
a = 13.3613
b = .04913


i'm not sure what you mean by y'.
it could be you mean y-hat.
if so, the regression equation is really y-hat = ...., which is shown as just y = 13.3613 + .04913x becomes:
the y-hat designation means that the value of y is based on the regression equation and is not an actual data point from the data set.


when x = 2, y = 13.3613 + .04913 * 2 which is equal to 13.45956.


here's a graph of the equation.


<img src = "http://theo.x10hosting.com/2024/041301.jpg">


here's the results.


<img src = "http://theo.x10hosting.com/2024/041302.jpg">


the results are:


r = .00348 which indicates a very weak positive correlation.
r^2 = .05899 which indicates that only about 6% of the value of y is explained by the correlation with the value of x which mean a very weak correlation.
f = .02095 which is not greater than the critical f value of 5.99.
this indicates the results are not significant which means there is insufficient data to conclude that a strong correlation exists.
p = .8896 which is significantly more than the critical p-value of .05 which, again, indicates that the results are not significant and therefore insufficient to determine that a strong correlation exists.


that's what i get from this analysis.