Lab 11 (4-15) - qtm lab assignment PDF

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Lab 11: Linear Regression 1. We will focus on the respogtfnse variable GPA. a. I made a histogram, which has a left skewed distribution

b. This data set has 207 observations

2. Examine the relationship between GPA and hrs extracurricular. a. I produced a histogram. The data is right skewed.

b. I produced a scatterplot. There may be a positive correlation.

c. The estimated correlation is 0.1646612, which is a weak positive correlation. The confidence interval is (0.02894107, 0.29442008). Because the p-value is less than 0.05 (0.01774), we reject the null hypothesis. 3. Estimate the linear regression equation that uses hrs_extracurricular to predict GPA (Model 1). a. ŷ = 3.106x - 2.874 b. Since the confidence interval of the intercept is (-11.7783691, 6.029595) and includes zero, the intercept is not significantly different than zero. c. Since the confidence interval of the slope is (0.5439825, 5.668140) and does not include zero, the intercept is significantly different than zero d. The R2 of the model is 0.02711, which is a weak association between hrs_extracurricular and GPA. e. The residual standard error is 7.38 on 205 degrees of freedom, which is high 4. For Model 1, check model assumptions using residual plots. a. No, it does not appear that the residuals are normally distributed because the data appears to be right skewed.

b. Produce a plot scatterplot with hrs_extracurricular on the x-axis and standardized residuals on the y-axis.

i. There is no evidence of a non-linear trend in the residuals ii. No, there is no evidence of a non-constant variance in the residuals 5. View information regarding student 1. a. Student 1’s GPA: 3.3, Student 1’s number of weekly hours spent on extra-curricular activities: 18 b. 7.375614 c. regular residual: 10.62439, standard residual: 1.443634 Based on Model 1, what was the residual for student 1? Regular and standard residuals both involve ŷ. However, regular residuals are y- ŷ, and standardized residuals are a quotient. d. Lower 6. Produce your own linear regression model to predict GPA using the other variables in the data set. Choose at least two independent variables. Your two variables can be either categorical or quantitative; however, if you chose to use a categorical variable you are responsible for correct

interpretation of the slope (which we did not discuss in class). Your model does not have to be the same for everyone in your lab group. a. I chose the variables sleep and number of hours on Facebook. There does not seem to be a correlation between sleep and GPA. However, I believe that as the number of hours spent of Facebook increases, GPA increases, meaning that there is a positive correlation between GPA and hours spent on Facebook. b. Slope for GPA and sleep: 0.2999 and the slope for GPA and hours spent on Facebook: 0.52285. There was a very weak positive correlation between GPA and sleep. Additionally, there was a moderately positive correlation between GPA and hours spent on Facebook. The hrs_facebook variable was a fairly significant predictor of GPA, but the sleep variable was not. c. The parameter estimates went in the direction that I anticipated. Although I did not think there would be any correlation between the sleep and GPA, the intercept still demonstrated the direction because it was a very small number. Since the slope for hours on Facebook in relation to GPA was about 0.5, the parameter went in the direction I anticipated in 6a. 7. R Code #distribution of SurveySp13 hist(SurveySp13$GPA) boxplot(SurveySp13) #cleaning GPA variable CleanSurveySp13...