![]() “Beauty in the classroom: Instructors pulchritude and putative pedagogical productivity”. Researchers at University of Texas, Austin collected data on teaching evaluation score (higher score means better) and standardized beauty score (a score of 0 means average, negative score means below average, and a positive score means above average) for a sample of 463 professors. However, the use of these student evaluations as an indicator of course quality and teaching effectiveness is often criticized because these measures may reflect the influence of non-teaching related characteristics, such as the physical appearance of the instructor. Many college courses conclude by giving students the opportunity to evaluate the course and the instructor anonymously. Therefore a simple least squares fit is not appropriate for these data. The residuals appear to be fan shaped, indicating non-constant variance. Below is a similar scatterplot, excluding District of Columbia, as well as the residuals plot. Would it be wise to use the same linear model to predict his wife's age? Explain.Įxercise 8.6.33 gives a scatterplot displaying the relationship between the percent of families that own their home and the percent of the population living in urban areas. You meet another married man from Britain who is 85 years old. What would you predict his wife's age to be? How reliable is this prediction? You meet a married man from Britain who is 55 years old. We might wonder, is the age difference between husbands and wives consistent across ages? If this were the case, then the slope parameter would be \(\beta_1 = 1\text\) what is the correlation of ages in this data set? Summary output of the least squares fit for predicting wife's height from husband's height is also provided in the table. The scatterplot below summarizes husbands' and wives' heights in a random sample of 170 married couples in Britain, where both partners' ages are below 65 years. Do you think the relationship between number of drinks and BAC would be as strong as the relationship found in the Ohio State study? Suppose we visit a bar, ask people how many drinks they have had, and also take their BAC. Calculate \(R^2\) and interpret it in context. The correlation coefficient for number of cans of beer and BAC is 0.89. Interpret the slope and intercept in context.ĭo the data provide strong evidence that drinking more cans of beer is associated with an increase in blood alcohol? State the null and alternative hypotheses, report the p-value, and state your conclusion. Write the equation of the regression line. Based on the scatterplot and the residual plot provided, describe the relationship between the protein content and calories of these menu items, and determine if a simple linear model is appropriate to predict amount of protein from the number of calories.ĭescribe the relationship between the number of cans of beer and BAC. Would it be appropriate to use this linear model to predict the height of this child?Įxercise 8.6.24 introduced a data set on nutrition information on Starbucks food menu items. Calculate the residual, and explain what this residual means.Ī one year old has a shoulder girth of 56 cm. The student from part (d) is 160 cm tall. Predict the height of this student using the model. Interpret the slope and the intercept in this context.Ĭalculate \(R^2\) of the regression line for predicting height from shoulder girth, and interpret it in the context of the application.Ī randomly selected student from your class has a shoulder girth of 100 cm. Write the equation of the regression line for predicting height. The correlation between height and shoulder girth is 0.67. The mean height is 171.14 cm with a standard deviation of 9.41 cm. The mean shoulder girth is 107.20 cm with a standard deviation of 10.37 cm. No, this calculation would require extrapolation.Įxercise 8.6.15 introduces data on shoulder girth and height of a group of individuals. Inference for the slope of a regression line.Fitting a line by least squares regression.Line fitting, residuals, and correlation.Comparing many means with ANOVA (special topic).Difference of two means using the \(t\)-distribution.Inference for a single mean with the \(t\)-distribution.Homogeneity and independence in two-way tables.Testing for goodness of fit using chi-square.Sampling distribution of a sample proportion.Case study: gender discrimination (special topic).Observational studies and sampling strategies.Case study: using stents to prevent strokes.OpenIntro, online resources, and getting involved. ![]()
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