Linear Regression Pt 2

T-Test

T-Test

Ho: B1 = 0

Ha: B1 =slash 0

P value greater than < .05

F-Test

H0: B1 = B2 = .. Br = 0

HA: B1 = B2 = … Br = 0 or Any combinations (At least one of the models variables is significant) SLASHES

T-Test vs. F-Test

F test is all of the variables, but T-Test you test significance of one variable

F statistics

Compares the model’s prediction to a model that contains no independent variables

H0

None of the independent variables are significant and has no explanatory power

H0 has no predictive relationship between

the x variables and Y in the population

H1

At least one of the coefficients of the independent variables is not equl to zero and has explanatory power

H1 model fits the data better than the

Intercept-only model

If F Significance is less than .05 you will

reject null hypothesis and pick the alternative

If significance F/P-Value <a then

reject the null hypothesis

whats the relationship btw carat weight n diamond price

Positive relationship

Interpretation on Carat weight

For each additional carat weight unit (x) we expect Diamond price (y) to go up 4318.79 dollars on average

95% weight is the

minimum and maximum range for carat weight (2011, 6626). If within this range if you see 0 that variable is not significant, IF you dont see 0 you can conclude the variable is statistically signfiicant.

P value is greater than .05

nonsignificant

as long as 0 is not included in the range its

valid (Value and Interval explanation)

Since the range does not have 0 we reject

null hypothesis and conclude age is statistically significant predictor/variable in predicting _____ // Age is statistically significant predictor for ___ //

Multiple R

Correlation Coefficient

R Square

Coefficient of Determination

Significance F

If entire model is statistically significant, if its less than .05

B0

Intercept

Year

B1

Y ^ =

B0 + B1 x

P val less than .05 and 95% range does not have a 0

//

P val is less than .05

Should not include 0

Interpret Coefficient estimate for slope (Predicting Electric Power demand per year)

For every year increase/additional year, we are expecting electric power demand increases by 10.53 units of the eletrical power (watts) on average.