Consider the following data x_i 1 1 2 2 2 3 y_i 1 2 0 4 4 9 Plot these data as a

Question

Consider the following data x_i 1 1 2 2 2 3 y_i 1 2 0 4 4 9 Plot these data as a scatter plot. Draw the best function of times to predict y. Is it linear What is its worth Obtain the least squares line Y^(x) equivalent l(x) and its worth. What are the point estimates of the response Y(4) and the mean response mu_y(4). Now assume the underlying model to be y = beta_0 + beta_1x + epsilon, where the distribution of the error epsilon is N(0, sigma^2). Give 95% confidence intervals for each of the four entities beta_0, beta_1, Y(4) and mu(4).

Explanation / Answer

Sol)

The regression equation is

y=a+bx

From excel

a) Scatter plot

b)

The fitted regression is y= -2.70588 +3.294 (x)

c) when x=4

then y= -2.70588 +3.294 (4) =10.47

d) 95% CI for intercept or b0 is -10.0326 and 4.621

95% CI for Slope is -0.44802, 7.036,

SUMMARY OUTPUT Regression Statistics Multiple R 0.773906 R Square 0.59893 Adjusted R Square 0.498663 Standard Error 2.268713 Observations 6 ANOVA df SS MS F Significance F Regression 1 30.7451 30.7451 5.973333 0.070899 Residual 4 20.58824 5.147059 Total 5 51.33333 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -2.70588 2.638876 -1.02539 0.363138 -10.0326 4.620813 X 3.294118 1.347816 2.44404 0.070899 -0.44802 7.036256

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.