Question

Please provide with R codes! thank you!!

Data:

Data: 179 161 162 605557 155 60 158 56 172 57 191 60 179 57 163 58 Height (cm) Head Circumference (cm)

Question:

Answer 1

> x=data$Height ## assume predictor as Height > y=data$Head.circumference ## assume response as Head circumference > ## 2 ) draw 3 most plots ## 1) scatter plot : > plot(x, y, main = "scatter plot") ## normality plot > qoplot(x,y, main="qqplot") > ## boxplot > boxplot (data,main="boxplot") ### from 3 plot we can say that there is no linear relationship between this two variables.

scatter plot 58 59 60 57 55 56 155 160 165 170 175 180 185 190

qqplot 55 56 57 58 59 60 Ooo 155 160 165 170 175 180 185 190

boxplot 180 140 100 60 Height Head. Circumference

> ### 3) numerically describe center, spread, and unusual points of the data / variables > mean(x) ## center [1] 168.8889 > var (x) ## spread [1] 144.8611 > mean(y) ## center [1] 57.77778 > var (y) ## spread [1] 3.444444 > summary(data) ## all summary of the data (center, spread, all ) Height Head.circumference Min. 155.0 Min. : 55.00 1st Qu. :161.0 1st Qu. : 57.00 Median : 163.0 Median : 57.00 Mean :168.9 Mean :57.78 3rd Qu. :179.0 3rd Qu.: 60.00 Max. : 191.0 Max. : 60.00 > ## 4) fit simple linear relationship between head circumference and height > fit = 1m(y-X) > fit call: Im(formula = y - x) Coefficients: (Intercept) 46.73442 0.06539

Coefficients: (Intercept) 46.73442 0.06539 > ### linear model : yhat = 46.73442 + 0.06539XX > Summary(fit) call: Im(formula = y - x) Residuals: Min 10 Median 3Q Max -2.2619 -1.0658 -0.3273 0.7764 3.1304 coefficients: Estimate Std. Error t value Pr>t (Intercept) 46.73442 8 .93447 5.231 0.00121 ** 0.06539 0.05278 1.239 0.25534 Signif. codes: O ****' 0.001 ***' 0.01 *' 0.05 '1' 0.1''1 Residual standard error: 1.797 on 7 degrees of freedom Multiple R-squared: 0.1798, Adjusted R-squared: 0.06265 F-statistic: 1.535 on 1 and 7 DF, p-value: 0.2553 > ## 5) regression paremater exact not zero > ## estimate of xis positive as x increase y value increases. > ## 6) residuls and it plot > res= fit$residuals > res 12 1.5610738 -2.2619367 -0.3 273250 3.1303931 -1.0657718 -0.9812081 0.7764142 -1.4389262 > plot(res) > ### points are scatter everywhere of the residual plot.

res -2 -1 0 1 2 3 NHO 4 Index CO 0

> ### 7) lurking variable is a variable that is not included as a exploratory or response > ## variable in the analysis but can affect the interpretation of the relationship between variable. > ## here may be age as a lurking variable, because height , and circumference is depend upon age > ### 8) example of pair of the regression model : height and weight is example > ## of the regression model here height or weight (choose) may be response variable > ## and explaratory variable.