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Local in the business of making bakery products wants to know whether there is any 2A company their products and the sale of those same products relabiounship betwe...

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Local in the business of making bakery products wants to know whether there is any 2A company their products and the sale of those same products relabiounship between the aount spent on adverusing collects information on 6 of the sales conducted in - the (usc & 05) To answer this question thc managet but close enough perhaps) Sales and advertising past thrce years (not exactly = random sarple of sales Values are in SIOOOs: (Ads: advertising expenditures; Sale$ sales during week of sale)Sale

local in the business of making bakery products wants to know whether there is any 2A company their products and the sale of those same products relabiounship between the aount spent on adverusing collects information on 6 of the sales conducted in - the (usc & 05) To answer this question thc managet but close enough perhaps) Sales and advertising past thrce years (not exactly = random sarple of sales Values are in SIOOOs: (Ads: advertising expenditures; Sale$ sales during week of sale) Sale 1 2 34 5 6 Ads X2 14 3 3 2 Sales$ Y 40 65 45 60 30 40 (a) Use & 0S and statistical test ofr (you can tun Excel regression analysis to get correlation t) to test the significance of the relationship. That is I5 this relationship (correlation) between advertising expenditures and sales statistically significant? If there is relationship: describe it in YOur own words Do test calculations by hand. Statistical Test ofr Hyps; HO HL: | 2. Test & Analysis: 3. Conclusion: (b) Use & =.05 and statistical test of slope b (you can use Excel regression output to get slope bl and SSE) to test the significance of the slope of the regression line. That Is_ can We use advertising expenditures to predict sales statistically? (Please calculate below Values by hand s0 that you can build your test statistic). Test of Slope 6 Hyps; HO HI: 2 , Test & Analysis Conclusion



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Use APPLE to verify some of the claims made in Section $6-3$ .
(i) Run the regression ecolbs on ecoprc, regprc and report the results in the usual form, including the $R$ -squared and adjusted $R$ -squared. Interpret the coefficients on the price variables and comment on their signs and magnitudes.
(ii) Are the price variables statistically significant? Report the $p$ -values for the individual tests.
(iii) What is the range of fitted values for ecolbs? What fraction of the sample reports ecolbs = 0?
Comment.
(iv) Do you think the price variables together do a good job of explaining variation in ecolbs? Explain.
(v) Add the variables faminc, hhsize (household size), educ, and age to the regression from part (i). Find the $p$ -value for their joint significance. What do you conclude?
(vi) Run separate simple regressions of ecolbs on ecoprc and then ecolbs on regpre. How do the simple regression coefficients compare with the multiple regression from part (i)? Find the correlation coefficient between ecoprc and regprc to help explain your findings.
(vii) Consider a model that adds family income and the quantity demanded for regular apples:
$e c o l b s=\beta_{0}+\beta_{1} e c o p r c+\beta_{2} r e g p r c+\beta_{3}$ faminc $+\beta_{4} r e g l b s+u$
From basic economic theory, which explanatory variable does not belong to the equation? When you drop the variables one at a time time, do the sizes of the adjusted $R$ -squareds affect your answer?

Part one. The results of the progression are Intercept is 1.9 estimate on Eco Price is -2.9 And the estimate on regular price is 3.03. And all of these estimates are highly significant. The r square is very low point 04 and r squared adjusted has similar value. We have 660 observations in our simple, so the simple is not small at all. This model is just not very good. The problem asks you to interpret the result, so this result is as predicted by economic theory. The own price effect is negative and the cross or substitute price effect is positive. An increase in echo price of 10 sense per pound Reduces the estimated demand for Eco label Apples by about .29. Mhm .29 lbs. An increase in regular price of 10 cents per pound for regular apples increases the estimated demand for eco labelled apples by about 0.3 The unit is pound. These effects are quite large in part two. So as I said earlier, each price bearable is individually significant, with a T statistic Greater than four in absolute value. The P values are essentially zero and we conclude that they are significant. Our tree, the fitted values has a minimum of 0.86 and the maximum of 2.09. This is much smaller range than e cole label pounds. The observed demand itself, Which ranged from 0 to 42, Although 42 is kind of an outlier, There are almost 2 50 observations with estimated no not estimated observed demand for eco label apples being zero and these observations are not accounted for in their predicted values. Our sixth, the r square is about 3.6%. This is very small. The model can only explain 3.6, less than 4% of the variation in the demand for eco label apples. The two price variables do not do a good job of explaining why demand varies across families. Part five. We add family income, household size, education and egg to you. Uh The regression that are square increased U exactly 4% and the adjusted osce square falls from point 0342 points 031 We can test the joint significance of the additional variable and the f statistic with four and 653 degrees of freedom has a P value of 0.63 So we are unable to retract the null hypothesis that the estimate on these variables are jointly uh equally zero or six. The problem asked you to run separate simple regressions of demand on price. Of eco labelled opposed and then demand on regular regular price. Yeah. I find that there are square in both cases to be very small, almost zero. And when you calculate the correlation coefficient between eco price and regular price, you would find The coefficient to be .83. So it is possible that the monte culinary t over these variables affect the fit of the model. In part seven we consider a model that adds family income and the quantity demanded for regular apples from basic economic theory. Okay, the regular the man does not belong to the equation. When we estimate the full model, we get our square of point oh six Adjusted r squared of .57 and we will drop the variables one at the time. So if we drop the price of eco labelled variable are square is .03 and at just the square is point 0 to 5. Then if we drop regular price It's just a square is .039. Oh regular, Our square is .039. It's just our square is .035 family income to be dropped. Our square is .06 at just a square is .056. Drop regular apple demand. Our Square is .038. It's just that our square is point oh 34 and all of these are smaller than there are square and adjusted r squared values from their full model. We conclude that the initial old model is still the best.


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