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Question 1

The mathematical expresion of the model is given by the equation,

Y = \(\beta_0 + \beta_1 X_1 + \epsilon\)

where \(X_1\) = father’s height and \(\epsilon\) = random error

Question 2

Galtons <- read.csv("/cloud/project/Galtons.csv")
reg <- lm(Height~Father,data=Galtons)
summary(reg)
## 
## Call:
## lm(formula = Height ~ Father, data = Galtons)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.2683  -2.6689  -0.2092   2.6342  11.9329 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 39.11039    3.22706  12.120   <2e-16 ***
## Father       0.39938    0.04658   8.574   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.446 on 896 degrees of freedom
## Multiple R-squared:  0.07582,    Adjusted R-squared:  0.07479 
## F-statistic: 73.51 on 1 and 896 DF,  p-value: < 2.2e-16

Question 3

Using the model fit, I think the model is useful, as the overall model is significant, F(2,895) = 54.69, p < .001

Question 4

My height = 70 inches Father’s height = 73 inches Mother’s height = 67 inches Parent’s Height = (73 + 67*1.08)/2 = 72.68 inches

From the model, My height = 39.11 + 0.40*72.68 = 68.18 inches

Question 5

The model underestimates my height by 1.82 inches.