Question

4. each 2 pts] Below is the R output for a simple linear regression model Coefficients: Estimate Std. Error t value Pr(>t) (Intercept) 77.863 4.199 18.544 3.54e-13 3.485 3.386 0.00329* 11.801 Signif. codes: 0 0.0010.010.05 0.11 Residual standard error: 3.597 on 18 degrees of freedom Multiple R-squared: 0.3891, Adjusted R-squared: 0.3552 F-statistic: 11.47 on 1 and 18 DF, p-value: 0.003291 (a) Write down the fitted model (b) We want to test H0 : β0-0 versus Hi : βο 0. Based on the p-value, make your decision (c) We want to test H0 : β1-0 versus Hi : βι 0. Based on the p-value, make your decision (d) Find a test statistic for H0 : β1-0. (e) Find the coefficient of determination (f) When 0, find the estimated mean of the response y (g) Find the standard error of β

R is a little difficult for me, please answer if you can interpret the R code, I want to learn better how to interpret the R code

Answer 1

a) Fitted model is y = 77.863 + 11.801 * x

b) Here p value for B0 is 3.54e-13 which is less than 0.05 so we reject the null hypothesis that B0 = 0.

c) Here p value of B1 is 0.00329 which is also less than 0.05 so we reject the null hypothesis that B1=0.

d) Test Statistic for B1 = 0 is

$t=\left ( \beta _{1}-0 \right )/S.E.(\beta _{1})$

e) Coefficient of determination is R_squared = 0.3891

f) When x =0 the estimated of y we simply get from the model in a). where we have to put the value of x = 0

therefore estimated of y is 77.863

g) Standard error of B1 is 3.485