1. Consider the following data set and the Minitab output. Derive (i.e,calculate

Question

1. Consider the following data set and the Minitab output. Derive (i.e,calculate) each number that has a superscript next to it in the upper right-hand comer. all of your work in complete detail. - Show Data Display Row X Y 1 3 14 2 5 16 3 720 4 5 13 5 8 19 6 9 23 7 10 24 8 14 22 9 20 38 10 22 39 Descriptive Statistics: X,Y variable NN Mean SE Mean StDev Minimum 01 Median 3 Maximum 10 0 10.30 2.03 6.43 3.005.008.50 15.50 22.00 10 0 22.80 2.86 9.05 13.00 15.50 21.00 27.50 39.00 Regression Analysis: Y versus X The regression equation is Y-8.860 + 1.353 x Coefficients Term Constant 8.86 1.64 Coef SE Coet T-Value P-Value 1.3534 0.1375 9.8 5.3910.00111 -2.64 64112 R-Sq- 92.4" R-sq ( adj ) -91.5t" s Analysis of Variance Source Regression 1 681.572 681.572 97.32 0.00024 Error Total DF MS 81 56.028 7.00322 9 737.6002 Prediction for Y Regression Equation Y 8.86 + 1.353 x Variable Setting 14 2 90180 .97312109 34.3142 Fit SE Fit 95% CI 958 PI Correlation: X, Y Pearson correlation of x and Y 0.9613

Explanation / Answer

### By using R command.

The superscripted value are represented by bold fo

> x=c(3,5,7,5,8,9,10,14,20,22)
> x
[1] 3 5 7 5 8 9 10 14 20 22
> y=c(14,16,20,13,19,23,24,22,38,39)
> y
[1] 14 16 20 13 19 23 24 22 38 39
> summary(x) ##Descriptive statistics of x.
Min. 1st Qu. Median Mean 3rd Qu. Max.
3.0 5.5 8.5 10.3 13.0 22.0
> summary(y) ##Descriptive statistics of y.
Min. 1st Qu. Median Mean 3rd Qu. Max.
13.00 16.75 21.00 22.80 23.75 39.00

> sdx=sqrt(var(x)) ## standard deviation of x
> sdx
[1] 6.429965
> sdy=sqrt(var(y)) ## standard deviation of y
> sdy
[1] 9.052931

> fit=lm(y~x) ## Regression of Y on X.
> fit

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept) x  
8.860 1.353  

> summary(fit)

Call:
lm(formula = y ~ x)

Residuals:
Min 1Q Median 3Q Max
-5.8076 -0.4241 0.7264 1.6512 2.0720

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 8.8600 1.6423 5.395 0.00065 ***
x 1.3534    0.1372 9.865 9.39e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.646 on 8 degrees of freedom
Multiple R-squared: 0.924, Adjusted R-squared: 0.9145
F-statistic: 97.32 on 1 and 8 DF, p-value: 9.394e-06

> anova(fit) ## ANOVA of Regression Model
Analysis of Variance Table

Response: y
Df Sum Sq Mean Sq F value Pr(>F)   
x 1 681.57 681.57 97.319 9.394e-06 ***
Residuals 8 56.03 7.00   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> cor(x,y) ## Correlation between X and Y.
[1] 0.9612701
>

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