Question

a) What is the formula for the estimated regression line?

(4 points + 1 point BONUS) There is some evidence to suggest that exposure to airborne fungal products may be associated with adverse health effects, for example, respiratory tract infections. A random sample of Canadian elementary schools was obtained and the following data was obtained for each: mesophilic fungi (y, in cfu/m5), building age (Age, x1, in years), air exchange rate (Rate, x2, per hour), indoor CO2 (CO2, x3, ppm), and outdoor temperature (Temperature, X4, C). The following are the results from R: Residuals: Min1Q Median 3 Max 68.80 -21.35 1.40 22.32 71.14 Coefficients: Estimate Std. Error t value Pr (>tI) (Intercept) 111.32601 35.05560 3.176 0.003944 ** 2.24456 0.56101 4.001 0.000494* 0.20778 3.49380 -0.059 0.953049 0.41631 0.05697 7.307 1.18e-07* Rate CO2 Temperature 0.755250.55682 1.356 0.187105 signif. codes : 0 ' , 0,001 '**, 0.01 '*' 0.05 .' 0.1 ' ' Residual standard error: 35.84 on 25 degrees of freedom (1 observation deleted due to missingness) Multiple R-squared: 0.8209, F-statistic: 28.65 on 4 and 25 DF, p-value: 5.185e-09 Adjusted R-squared: 0.7923

b) Is the overall regression significant at a significance level of 0.01? Hint: Perform an F test at a significance level of 0.01. No work is required because all of the numbers can be obtained from the computer output.

c) Which of the variables are linearly associated with the fungi concentration assuming that the rest of the variables are in the model? You may assume a significance level of 0.01. You do not have to perform any significance tests but you have to explain how you arrive at your answer.

d) Assuming that the variables are named as specified in the question and the variables are in a table called "fungi", what is the code that was used to generate the output above?

Answer 1

а. У= 111.32601 + 2.2445621-0.20778T2+0.41631x3+0.75525x4 b. Value of F statistic =28.65 p - value 5.18 x 109 0.01 hence overall regression is signi ficant at a significance level 0.01. C. Age is significant since p-value = 0.000494 < 0.01 CO2 is significant since p-value = 1.18 × 10-7 < 0.01 Other cariables are insignificant since is significant since their p - value > 0.01

d. R code: summary(lm(fungi~(Age+Rate+CO2+Temperature)))