Question

STAT 201-001 Winter 2017-2018 Extra credit VIII (5 points) Due: 6:00PM Wednesday. March 21 2018 Name: ID.#: All the extra credit assignments must be neatly hand written on the cover sheet or typed on 8 % by 11 inel paper. This cover sheet must be attached and stapled to the front of your work. Paper clips and foldin over corners will not be accepted. All extra credit assignments are expected to be handed in on the du date to receive credit. Problem #1. The following data show the dollar value of sales with corresponding advertising levels for a small retail chain in Philadelphia. Advertising Sales $6445 $4015 $4822 $7017 $2848 $3888 $5554 $584 $386 $452 $635 $242 $328 $517 a) Plot these data in the form of scatter diagram. Does the linear model appear to be appropriate for estimating sales as a function of dollars spent on advertising? b) Based on a regression analysis, what is the estimated increase in the amount of sales per every extra dollar in advertising? c) What would be the value of estimated sales if advertising expenditures were $622? (To the nearest S100) d) What is an estimate of the standard deviation of error term in the regression model? (To the nearest $100). e) Test whether a linear relationship exists between advertising and sales. f Find the approximate p-value for the test statistics. Find the upper bound of a 95% confidence interval for the increase in the amount of sales per extra dollar in advertising. (To nearest S). g) h) Find the percentage of variation of amount of sale that can be explained by changes in advertising. i) Find estimated correlation coefficient.

Answer 1

a) Following is the scatter plot 6,000 4,000 2,000 200 300 400 500 600 700 Advertising, (x) The linear model seems toe appropriate b) 5846445 3763880 341056 41538025 386 452 635 242 328 40151549790 148996 16120225 48222179544 204304 23251684 7017 4455795 403225 49238289 2848 689216 585648111104 3888 1275264 107584 15116544

517 5554 2871418 26728930846916 3144 34589 16784907 1531018 184222787 Least Squares Regression Equation : У-Do + bIX 7(16784907) - (3144)(34589) 7(1531018) - (3144)2 117494349-108747816 8746533 832390 10.507734 10.5077 107171269884736 Slope term, b 10.5077 Slope of (10.507734) implies that for every 1 unit increase in Advertising (x), we expect an increase of 10.507734 in Sales (y). Estimated increase in amount of sales per extra dollar in advertising is 10.5077 C) 34589 3144 (10.507734)221.811884 221.8119 Intercept term, bo 221.8119 Least Squares Regression Eq": у-22 1.81194 (10.5077):

atx -622, y is estimated by: у (221.8119) + (10.5077)(622) x-622 6757 .62 6800 6757622653 6757.6227 1531018 (3144)2 118912.857143 - 184222787 13308655.428571 ( y) 16784907 (3144) (34589 1249504.714286 SST - SSvv- 13308655.428571 SS2 1249504.7142862 SSxx118912.857143 13129463613397 SSE- SST - SSR 13308655.428571 13129463.613397 Standard Error of the Estimate Estimate of ơ is called Standard Error, and is given by: 179191.815174 SE 179191.815174 7-2 189.310230 189.3102 Se 189 200 The average distance from observed values to regression line is 189.3102 By Chegg's rules, we can solve only four sub-parts in case of multiple parts