8.2 Baby weights, Part II.

(a) Write the equation of the regression line

y^=po+p1X

(b) Interpret the slope in this context, and calculate the predicted birth weight of first borns and others.

y^=120.07-1.93x

(c) Is there a statistically significant relationship between the average birth weight and parity?

Ho:P1 =0 Ha:P1 != 0

since the p value = 0.1052, It is more 0.05, we fail to reject the null hypothese

8.4 Absenteeism

(a) Write the equation of the regression line.

y=18.93-9.11X1+3.1X2+2.15X3

(b) Interpret each one of the slopes in this context.

  1. 9.11 days less if student not aboriginal
  2. 3.1 days more if it is male,
  3. 2.15 days more if it is slow learner.

(c) Calculate the residual for the first observation in the data set: a student who is aboriginal, male, a slow learner, and missed 2 days of school.

the residual is -22.18 days.

(d) The variance of the residuals is 240.57, and the variance of the number of absent days for all students in the data set is 264.17. Calculate the R2 and the adjusted R2. Note that there are 146 observations in the data set.

R2 <- 1-(240.57/264.17)
R2
## [1] 0.08933641
adjustedR2 <- 1-(240.57/264.17)*((146-1)/(146-3-1))
adjustedR2
## [1] 0.07009704

8.8 Absenteeism, Part II.

The one should be removed is the no learnerstatus.

8.168.16 Challenger disaster, Part I

(a) Each column of the table above represents a di???erent shuttle mission. Examine these data and describe what you observe with respect to the relationship between temperatures and damaged O-rings

It seems like lower temperture has more damaged.

(b) Failures have been coded as 1 for a damaged O-ring and 0 for an undamaged O-ring, and a logistic regression model was fit to these data. A summary of this model is given below. Describe the key components of this summary table in words.

the damaged decreased by 0.2162 when the temperature increase by 1 degree.

(c) Write out the logistic model using the point estimates of the model parameters.

y= 11.663-0.2162Xtem

d) Based on the model, do you think concerns regarding O-rings are justified? Explain

Yes, since P value is 0, which means significant.

8.18 Challenger disaster, Part II

(a)

P51=0.6536388, p53=0.5504788, P55=0.4427862

(b) Add the model-estimated probabilities from part (a) on the plot, then connect these dots using a smooth curve to represent the model-estimated probabilities.

tem <- c(51,53,55,57,59,61,63,65,67,69,71)
p <- c(0.6536388,0.5504788,0.4427862,0.340649,0.25109,0.17869,0.123727,0.08393,0.056126,0.0371548,0.0244302)
plot(tem,p,type="o")

(c) Describe any concerns you may have regarding applying logistic regression in this application,and note any assumptions that are required to accept the modelโ€™s validity.

My concerns is temputure is the only independent variable, we may need to consider other variables in account.