Stats Help Regression Line Here is the data Assume that the

Stats Help! (Regression Line)

(Here is the data)

Assume that the sample in the table above was drawn from a bivariate normal distribution.

a) Compute the sample coefficient of determination, the proportion of variation \"explained\" by simple linear regression.

b) Construct an analyis of variance table for testing H0: ?_{1 =}0 _VS H1: ?₁ ?0. Do these data provide convincing evidence that knowing x helps one predict y? (Assumer a significance level of a=0.05)

c) Construct a 0.95-level confidence interval for the slope of the population regression line for predicting y from x.

Thank you!

Solution

We got regression output from excel,

    30

ANOVA




                     df          SS           MS               F            Significance F
Regression   1     946.8925    946.8925   34.37557     2.65E-06
Residual    28    771.2742 27.54551
Total            29    1718.167

                   Coefficients     Standard Error    t Stat        P-value       Lower 95%      Upper 95%
Intercept   -71.3706 18.36648    -3.88592      0.00057      -108.993     -33.7486
X Variable1 0.742661      0.126668         5.863068      2.65E-06    0.483194        1.002128

a) coefficient of determination = R² = 0.55

i.e. 55% variations are explained by simple linear regression.

b)

H0: _{1 =}0 _VS H1: ₁ 0.

From ANOVA table we got , p value =2.65E-06

We have significance level of a=0.05

p value < a, hence we reject null hypothesis.

Data provide convincing evidence that knowing x helps one predict y

C) 95 % confidence interval is given by,

(0.483194, 1.002128)