Question

Do the linest fit, and match each statistical quantity with its value Question 1 options: 1.997 7 8.81 0.16 3.86 0.86 1. The slope (gradient) of the line 2. The y-intercept which is the value of y when x=0 3. The standard error value for the slope value 4. The standard error value for the y-intercept 5. The number of degrees of freedom 6. The residual sum of squares Question 2 (1 point)

Answer 1

Explanation:

Hello!

Full text in attachment.

Given the data of the dependent variable Y and the independent variable X,

you have to estimate the linear regression: ^Y= a + bX

Where "a" is the estimate of the intercept and "b" is the estimate of the slope.

n= 9

∑X= 42.70; ∑X²= 250.45; ∑Y= 120.05; ∑Y²= 1801.03; ∑XY= 665.16

Y[bar]= 13.34; X[bar]= 4.74

Using the software I've calculated the asked values:

The slope of the line is
`b= (sumXY-((sumX)(sumY))/(n) )/(sumX^2-((sumX)^2)/(n) ) = (665.16-(42.70*120.05)/(9) )/(250.45-((42.70)^2)/(9) ) = 1.997`

The value of the Y-intercept is a= Y[bar] -bX[bar]= 13.34-1.997*4.74= 3.86

The standard error of the slope is Sb= 0.16

The standard error of the Y-intercept is Sa= 0.86

The degrees of freedom for the hypothesis test for the slope (t-test) are n-2= 9-2= 7

The SSresidues= 8.81

I hope this helps!