Task C



•    Relationship between mean age of children in a family and height of Christmas tree was
studied. The resulting data were following:

















•    Does the age of children in family affect the height of the Christmas tree bought by the
parents?

Null hypothesis

•    There is no correlation between the height of Christmas tree and the age of the children.

R script

•    tree<-read.delim2("clipboard")

•    cor.test(tree$tree.height, tree$age)

•    lm.c<-lm(tree$tree.height~tree$age)

•    summary(lm.c)

•    ggplot(data=tree, aes(x=age, y=tree.height))+geom_point()+

•      geom_smooth(method="lm", color=1)+

•      labs(x="Age", y="Tree height")+theme_classic()

Results

•       Pearson's product-moment correlation



•    data:  tree$tree.height and tree$age

•    t = -3.8541, df = 8, p-value = 0.004849

•    alternative hypothesis: true correlation is not equal to 0

•    95 percent confidence interval:

•     -0.9523889 -0.3585995

•    sample estimates:

•           cor

•    -0.8061992

Results

•    Call:

•    lm(formula = tree$tree.height ~ tree$age)



•    Residuals:

•         Min       1Q   Median       3Q      Max

•    -0.78154 -0.35686 -0.03737  0.46167  0.56491



•    Coefficients:

•                Estimate Std. Error t value Pr(>|t|)

•    (Intercept)  2.99572    0.34361   8.718 2.34e-05 ***

•    tree$age    -0.10968    0.02846  -3.854  0.00485 **

•    ---

•    Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1



•    Residual standard error: 0.5001 on 8 degrees of freedom

•    Multiple R-squared:   0.65,    Adjusted R-squared:  0.6062

•    F-statistic: 14.85 on 1 and 8 DF,  p-value: 0.004849



Conclusion

•    There is a negative linear regression between the age of children and the tree height.