10-46. INTERPRETING REGRESSION RESULTS, MATCHING TIME PERIODS. Nandita Summers works at Modus, a store that caters to fashion for young adults. Nandita is responsible for the store's online advertising and promotion budget. For the past year, she has studied search engine optimization and has been purchasing keywords and display advertising on Google, Facebook, and Twitter. In order to analyze the effectiveness of her efforts and to decide whether to continue online advertising or move her advertising dollars back to traditional print media, Nandita collects the following data: Online Sales Month Advertising Expense Revenue September $5,125 $44,875 October 5,472 42,480 November 3,942 53,106 December 1,440 64,560 January 4,919 34,517 February 4,142 59,438 March 1,290 51,840 April 5,722 36,720 May 5,730 62,564 June 2,214 59,568 July 1,716 35,450 August 1,875 36,211 Required 1. Nandita performs a regression analysis, comparing each month's online advertising expense with that month's revenue. Verify that she obtains the following result: Sales revenue = $51,999.64 - (0.98 x Online advertising expense) Variable Coefficient Standard Error t-Value Constant $51,999.64 7,988.68 6.51Independent variable: Online advertising expense -0.98 1.99 -0.49 72 = 0.02; DurbineWatson statistic = 2.14 2. Plot the preceding data on a graph and draw the regression line. What does the cost formula indicate about the relationship between monthly online advertising expense and monthly sales revenue? Is the relationship economically plausible? 3. After further thought, Nandita realizes there may have been a flaw in her approach. In particular, there may be a lag between the time customers click through to the Modus website and peruse its social media content (which is when the online ad expense is incurred) and the time they actually shop in the physical store. Nandita modifies her analysis by comparing each month's sales revenue to the advertising expense in the prior month. After discarding September sales revenue and August advertising expense, show that the modified regression yields the following: Sales revenue = $28,361.37 + (5.38 x Online advertising expense) Variable Coefficient Standard Error t-Value Constant $28,361.37 5,425.69 5.22 Independent variable: Previous month's online advertising expense 5.38 1.31 4.12 2 = 0.65; Durbin-Watson statistic = 1.71 4. What does the revised formula indicate? Plot the revised data on a graph. Is this relationship economically plausible? 5. Can Nandita conclude that there is a cause-and-effect relationship between online advertising expense and sales revenue? Why or why not