The objective of commercials is to have as many as viewers as possible remember the product in a favourable way and eventually buy it. In an experiment to determine how the length of a commercial affects people's memory of it, 50 randomly selected people were asked to watch a half-hour TV show. In the middle of it, a commercial advertising of a brand-new product appeared. Each viewerwas exposed to varying lengths of the commercial, ranging between 20 to 60 seconds, but its essential content was the same. Aer the TV show fmished, each person took a test to determine how much heishe remember about the product. The commercial times (CT) and test scores (TS) (on a 30-point test) are recorded. A simple regression model of the form: 1E; Ba + mch + g, i=Li,52, was estimated with the least squares method and an excerpt from the output is shown partially as follows: Regression Statistics Ohlervntiom 52 ANOVA df 55 MS F Regreslinn 848 Redd u El 1481 Total Coefficients Standard Ennr t Stat Pevalue Intercept 2.501 2.229 1.167 CT 0. 286 0. 1 15 2.487 Answer the following questions, using the above information 1 Briey describe the least squares method for estimating the regression model in plain English (without math equations). 2 There are assumptions required for the regression error. Apart from zero mean, normality, and constant variance assumptions, what are the remaining two assumptions? 3 Determine the dependent and independent variable of the model and write down the estimated regression equation. 4 Interpret the estimated slope coefcient ([31). 5 Is there enough evidence to support a positive effect at the 1% signicance level? Justify. [6] Compute the 95% condence interval for the slope parameter of the regression model. Show your work and interpret the intervaL [7] Describe the following three statistics: the sum of squared total, the sum of squared regression, and the sum of squared errors. Find the value of each of these three statistics. [8] Find the values of the coecient of correlation and the coeicient of correlation. Show your work and interpret the results. [9] Forecast the test score when the length of TV commercial is 40 seconds based on the estimated regression model. Show your work. [10] One experiment participant was exposed to the TV commercial for 55 seconds and the participant's test score was recorded as 12. Based on the estimated regression model, compute the regression error (residual) of the participant. Show your work