Subject: Mathematics / Statistics
QuestionNote: use Rstudio to work those problems out including the main questions by showing me the steps of how to get the data per Mosaic data set questions throughout questions 6 – 11 since I have trouble accessing the data through the mosaic data files. Show all the work from the Rstudio. If you don’t have Rstudio, install it on your PC.Answer the multiple choice questions as you work the problem out.In the Mosaic data set CoolingWater, water was poured into a mug and a temperature probe inserted into the water with a few seconds of the pour. The time in minutes, time, and the temperature in Celsius, temp, were recorded.6. Find the equation of the LSRL for this data.a. yˆ = 64.27? 0.22xb. yˆ = 64.27 + 0.22xc. yˆ = 255.66 ? 3.60xd. yˆ = 3.60 + 0.22xe. none of these7. Plot the residuals for the CoolingWater data. What does the pattern of the residuals tell you about the linear model?a. The evidence is inconclusive.b. The residual plot confirms the linearity of the model.c. The residual plot does not confirm the linearity of the model.d. The residual plot clearly contradicts the linearity of the model.e. none of theseUse the variables temp (average outdoor temperature in F for a billing cycle) and kwh (the electricity usage for a billing cycle) from the data set called Utilities (from Mosaic data) for problems 8-11.8. Which variable should be the explanatory variable?a. tempb. kwh9. What is the value or the coefficient of determination?a. -0.0798778b. 0.0063805c. 0.9201222d. 0.0798778e. none of these10. What is the residual plot for this data? Note: Draw and reveal the graph for this data11. Would you conclude that this LSRL is a good model?a. Yesb. No12. Simpson’s Paradox occurs whena. There is a reversal in direction of a comparison when data is transformed with powers.b. There is a reversal in direction of a comparison when data from several groups is combined.c. A conditional distribution gives a contradictory answer.d. The LSRL is used to predict data that is far from the other explanatory values.e. None of these.