please answer
An advertising rm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it has conducted. The rm has collected bivgriate data on 15 of its recent campaigns, including the cost of each campaign (denoted by x, in millions of dollars) and the resulting A percentage increase in sales (denoted by y). For the data, the leastsquares regression equatign is y = 6.18 + 0.17x. One client plans to spend about 4.8 million dollars on advertising and would like to know what kind of increase in sales she can expect after spending that amount. The rm has used the regression equation to predict the resulting percentage increase in sales for this client, but the firm also would like a prediction interval for the client's resulting percentage increase in sales and a condence interval for the mean percentage increase in sales for clients spending this same amount. The rm has computed the following for its data. - mean square error (MSE) % 0.042 1 (4.3 Dz - E + 15 a 0.3806, where x1, x2, ..., x15 denote the sample campaign costs, and ; denotes their mean 2 (xi-'32 :'= 1 Based on this information, and assuming that the Egrgssion assumptions hold, answer the questions below. {If necessary, consult a list of formulas.) (a) What is the 90% prediction interval for an individual value for percentage increase in sales when the campaign cost is 4.3 million dollars? (Carry your intermediate computations to at least four decimal places, and round your answer to at least two decimal places.) Lower limit: [I Upper limit: I] (b) Consider {but do not actually compute) the 90% condence interval for the mean percentage increase in sales when the campaign cost is 4.8 million dollars. How would the prediction interval computed above compare to this condence interval (assuming that both intervals are computed from the same sample data)? 0 The prediction interval would have the same center as, but would be narrower than, the condence interval. 0 The prediction interval would be identical to the condence interval. 0 The prediction interval would be positioned to the left of the confidence interval. 0 The prediction interval would be positioned to the right of the condence interval. 0 The prediction interval would have the same center as, but would be wider than, the condence interval. (c) For the campaign cost values in this sample, 6.9 million dollars is more extreme than 4.8 million dollars is, that is, 6.9 is farther from the sample mean campaign cost than 4.8 is. How would the 90% prediction interval for the mean percentage increase in sales when the campaign cost is 4.8 million dollars compare to the 90% prediction interval for the mean percentage increase in sales when the campaign cost is 6.9 million dollars? 0 The intervals would be identical. 0 The interval computed from a campaign cost of 4.8 million dollars would be wider and have a different center. O The interval computed from a campaign cost of 4.8 million dollars would be wider but have the same center. 0 The interval computed from a campaign cost of 4.8 million dollars would be narrower but have the same center. 0 The interval computed from a campaign cost of 4.8 million dollars would be narrower and have a different center
