Malak Alammar Lab 12 1. State the specific research question (related to the interaction effect) that you are going to attempt to answer with your analysis. It should be clear from reading your research question which variables you are analyzing. a. Is there an interaction between whether it's a working day and feeling temperature (Celsius) on the number of riders who use the company’s bikes on a given day? 2. Briefly explain who the stakeholders are for this analysis. a. The stakeholders for this analysis are the biking companies. 3. Run a general linear model to answer your research question. Write a set of hypotheses for the interaction effect, confirm relevant assumptions, and write a full conclusion for the interaction effect in context. Also interpret the appropriate effect size for your model in context. a. Assumptions i. Random Sample ii. Independent Observations iii. Numeric variable is linearly related to response variable i. Normal Residualsi. Equal Variance i. Hypothesis 1. H0: There is no interaction between working day and feels like temperature on a ridership. 2. HA: There is an interaction between working day and feels like temperature on a ridership.ii. Conclusion There was no significant interaction between working day and feels like temperature on ridership (t = -0.525, df = 199, p = .600) 4. If your interaction effect was significant, write a brief statement about what its slope estimate means in the context of the data. If your interaction was not significant, briefly discuss the slope estimates of the main effects of your two explanatory variables and whether or not they can tell you anything about daily ridership for this bikeshare company (you do not need to write a formal conclusion for each main effect, but rather talk about the significance/non-significance and direction of the slope estimates in context). a. The slope for a working day is positive and the reference point is “yes,” which means that ridership is higher (but not significantly) by 66.95 riders on working days than on non-working days. b. The slope for feels like temperature is positive and the variable is mean centered. So as the temperature increases, the ridership significantly increases. 5. What limitations are there to your results? Include one possible confounding variable and what impact it might have on the results.a. One limitation within the results is that even though the effect of feeling temperature was significant, the true weather conditions on each given day were not taken in account-- though true weather data was collected, it was not utilized as two other explanatory variables were picked. For example, high feeling temperatures cannot tell us if the weather was optimal for bike riding. It could have been very hot, but there also could have been intense showers as well. 6. What implications can you draw from your results? How might these findings be used by the study’s stakeholders? a. The effect of working day on ridership does not depend on the feels like temperature; however, feels like temperature while holding working day constant was a significant linear predictor of ridership. Thus, the company can consider this as an explanatory variable for predicting future ridership. b. We can also implicate that since our results yielded a positive slope value for feeling temperature and ridership, these two variables are directly related.R Code: > getwd() > bikes <- read.csv("Lab12_bikeshare.csv") > bikes$feelslike_c <- bikes$feelslike - mean(bikes$feelslike) my_glm <- lm(ridership ~ workingday * feelslike_c, data = bikes) > plot(bikes$feelslike_c, bikes$ridership, xlab = "Feeling temperature (Celsius)", ylab = "Total number of rides taken", main = "Feeling temperature and total number of rides taken", pch = 20) > hist(my_glm$residuals, main = "Model Residuals", xlab = "Residual", col = "light grey", right = F) > plot(my_glm$fitted.values, my_glm$residuals, xlab = "Fitted Values", ylab = "Residuals", main = "Residual Plot", pch = 20) > abline(h=0, col = "red") > summary(my_glm) Call: lm(formula = ridership ~ workingday * feelslike_c, data = bikes) Residuals: Min 1Q Median 3Q Max -4517.1 -1090.2 -99.2 1054.8 4425.6 Coefficients: Estimate Std. Error (Intercept) 4435.73 191.65 workingdayyes 66.95 236.71 feelslike_c 121.96 16.54 workingdayyes:feelslike_c -11.32 21.56 t value Pr(>|t|) (Intercept) 23.145 < 2e-16 *** workingdayyes 0.283 0.778 feelslike_c 7.372 4.42e-12 *** workingdayyes:feelslike_c -0.525 0.600 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1Residual standard error: 1602 on 199 degrees of freedom Multiple R-squared: 0.3741, Adjusted R-squared: 0.3646 F-statistic: 39.64 on 3 and 199 DF, p-value: <