Question

Given are five observations for two variables, 7 and y. 2 1 3 4 S M 3 7 5 11 14 The estimated regression equation is y = 0.2 +2.67 a. Compute the mean square arror using the following equation to 3 decimals), - MSE SSE - 2 b. Compute the standard error of the estimate using the following equation (to 3 decimals). 5 VMSE SSE N-2 c. Compute the estimated standard deviation by using the following equation (to 3 decimals). $ sh V2(x - 2) d. Use the t test to test the following hypotheses (a -0.05 ): H: = 0 H.: +0 Compute the value of the test statistic (to 2 decimals). The p-value is between 0.025 and 0.05 V Use Table 1 of Appendix B. What is your conclusion? Conclude a significant relationship it between xandy e. Use the F test to test the hypotheses in part (d) at a 0.05 level of significance. Complete the table below. Calculate the sum of Squares (to 1 decimal), the Mean Squares (to 3 decimals), and the ratio (to 2 decimals). Source of Variation Degrees of Freedom Sum of Squares F Mean Square p-value

Answer 1

SSE 11-1 (y -ýt I=1

A B с D у <> ŷ - y 1 2 E (-y)? =POWER(D3,2) -0.2 0.04 -1.6 2.56 9 -0.4 0.16 -0.8 0.64 12.4 =SUM(E3:57) =0.2+2.6*A3 =C3-B3 3 2.8 7 5.4 5 8 11 10.6 14 13.2 SSE => 3 3 4 5 1 x 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2 S = MSE = 4.133 =E8/3 S = VMSE 2.033 =SQRT(E14)

A B 1 x <> у 2 3 C y - =0.2+2.6*A3 =C3-B3 2.8 5.4 1 3 4 7 1 2 3 E F. (y - 2 (x; - x)? =POWER(D3,2) =POWER(A3-$A$8,2) -0.2 0.04 4 -1.6 2.56 9 0 -0.4 0.16 1 -0.8 0.64 4 12.4 10 =SUM(E3:E7) Elx; - x)? 5 3 5 00 6 4 11 7 14 5 3 10.6 13.2 SSE => 8 9 x = 3 10 11 12 Standard Error = Sb1= 0.643 =E17/SQRT(F8) 13 52 MSE = 4.133 =E8/3 14 15 16 17 18 19 S = VMSE = 2.033 =SQRT(E14)

(d)

Test statistic. The test statistic is at statistic (t) defined by the following equation. t = b / SE where by is the slope of the sample regression line, and SE is the standard error of the slope.

t = 2.6 / 0.643 = 4.044

(e)

Go to data ⇒ then data analysis toolpak in Excel

And select regression.

AutoSave Off H9 x x Book1 - Excel Mr. Mayank Dugar MM File Home Insert Page Layout Formulas Data Review View Help Search Share Comments AL 即回 Queries & Connections B Properties B Edit Links e là Clear Reapply Advanced Data Analysis ?, Solver Stocks Sort Outline Get Data Geography = Filter Refresh All- ZL. Text to Columns - What If Forecast Analysis – Sheet Forecast Get & Transform Data Queries & Connections Data Types Sort & Filter Data Tools Analyze J7 Х fix А. B c D G H J к L M N O P 1 x <> у y - (y - y)^ X 2 3 4 =0.2+2.6*A3 =C3-B3 2.8 E F (x1 - x)? =POWER(D3,2) =POWER(A3-$A$8,2) 0.04 4 2.56 1 1 OK 3 7 -0.2 -1.6 2 5.4 Cancel 8 9 0 Data Analysis Analysis Tools Covariance Descriptive Statistics Exponential Smoothing F-Test Two-Sample for Variances Fourier Analysis Histogram Moving Average Random Number Generation Rank and Percentile Regression 3 -0.4 -0.8 0.16 1 10.6 13.2 Help 7 4 0.64 12.4 SSE => 10 [(x; - x)? =SUM(E3:E7) 0.643 =E17/SQRT(F8) 5 3 5 6 4 11 5 14 8 3 9 = 3 10 11 12 Standard Error = Sb1= 13 14 s? 15 16 17 S = 18 19 20 Sheet2 Sheet1 MSE = 4.133 =E8/3 VMSE = 2.033 =SQRT(E14) + Ready 5 + 110% I Type here to search ORI E W х A B (» ENG 10:27 PM 31-Jul-20

Enter the values shown below and click ok.

Regression ? Х OK Input Input Y Range: Input X Range: SBS1: SBS6 Cancel SA$1:$A$6 Help Labels Confidence Level: Constant is Zero 95 Output options Output Range: New Worksheet Ply: O New Workbook Residuals Residuals Standardized Residuals Residual Plots Line Fit Plots Normal Probability Normal Probability Plots

you will get the f test values in a new sheet with the heading anova table.

F test values.

Significance f is the p value

ANOVA df SS Significance F 0.027214829 1 MS F 67.6 67.6 16.35483871 12.4 4.133333333 Regression Residual / Error Total 3 st 80

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