Question

# Given are five observations for two variables, x and y . xi 1 2 3 4...

Given are five observations for two variables, x and y .

 xi 1 2 3 4 5 yi 53 58 47 21 11

Use the estimated regression equation is y-hat = 78.01 - 3.08x

A.) Compute the mean square error using equation.

s^2 = MSE = SSE / n -2

[     ]   (to 2 decimals)

B.) Compute the standard error of the estimate using equation

s = sqrtMSE = sqrt SSE / n - 2

[      ] (to 2 decimals)

C.) Compute the estimated standard deviation of b1 using equation.

sb1 = s / sqrt ( xi - x-bar )^2

[       ] (to 4 decimals)

D.) Use the t -test to test the following hypotheses (a=.05 ):

H0 = B1 = 0

Ha = B1 ≠ 0

Compute the value of the -test statistic (Enter negative values as negative numbers). [          ] (to 4 decimals)

THE P-VALUE IS: [ Less than .01, * between .01 and .02, * .02 and .05, * .05 and .10, * .10 and .20, * .20 and .40, * Greater than .40. ]

What is your conclusion? [ DO NOT REJECT ; REJECT ] Ho

E.)

Use the F -test to test the hypotheses in part (d) at a .05 level of significance. Present the results in the analysis of variance table format.

Complete the F table below. Calculate the Sum of Squares (to 1 decimal), the Mean Squares (to 1 decimal), and the F ratio (to 2 decimals).

 Source of Variation Degrees of Freedom Sum of Squares (to 1 decimals) Mean Square (to 1 decimals) (to 2 decimals) -value (to 4 decimals) Regression Error Total

What is the P -value? [ between .01 and .025 ; *between .025 and .05 ; * between .05 and .10 ; * greater than .10 ; * Lower than .01 ]

What is your conclusion, based on this F test?

We [ DO NOT REJECT ; REJECT ] Ho

E)

 ANOVA Sourse df SS MS F P-value Regression 1 1464.1 1464.10 16.90 0.0261 Residual 3 259.9 86.63 Total 4 1724

The p-value is between .025 and .05.

The P-value from the t-test in D) should be equal to the P-value in E). The correct regression equation is y^ = 74.3 - 12.1 xi.

From D), we retain the Ho and conclude that the variable X does not have a significant effect on Y at 0.05 level of significance. Whereas from E), we reject Ho and conclude that the variable X has a significant effect on Y at 0.05 level of significance.

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