ductory Statistics Third Edition Perdisco Assessment Below is a set of assessable homework questions on this topic, selected by your professor. Take care! Do not submit your answers until you have read all the instructions and answered the questions carefully. When you submit your answers, you will receive immediate feedback. Navigating this page: Submit answers: Submit your answers for immediate grading Bookmark: Save this question set so that you can come back to it later 1 of 3 ID: MST.FET.R.RF.01.0010A [3 marks] marks] A regression equation has been developed in order to help predict the amount of sales made in a clothing store each day (Y) based on the number of square feet covered by the store's floor space (X). A sample of 100 similar clothing stores is collected, with floor spaces ranging from 100 square feet to 300 square feet. For each store, the floor space (in square feet) and the amount of sales made that day (in dollars) are recorded. The following regression equation is calculated: ^ y = 2,096 + 53x Select whether or not each of the following conclusions are correct from the regression analysis: Correct a) If the floor space of a store were to increase by one square foot, the predicted increase in sales would be $2,096. b) If a store has a floor space of 75 square feet, the predicted sales in a day is $6,071. c) If a store has a floor space of 175 square feet, the predicted sales in a day is $11,371. 2 of 3 Not correct ID: MST.FET.R.RF.02.0040A [1 mark] mark] In simple linear regression, a common measure is the one given by the following formula: ^ (yi - yi)2 Select the correct interpretation of what this formula means to the regression model: It is the amount of variation in the response variable that is accounted for by the explanatory variable. It is the amount of variation in the response variable that is not accounted for by the explanatory variable. It is the amount of variation in the explanatory variable that is not accounted for by the response variable. It is the amount of variation in the explanatory variable that is accounted for by the response variable. 3 of 3 ID: MST.FET.R.RF.03.0040A [1 A simple linear regression equation is to be constructed mark] mark] to determine if there is a linear relationship between a response variable (Y) and an explanatory variable (X). A random sample of size n has been collected and the values xi and yi for i = 1, 2, ..., n have been recorded. The residuals (ei) in this analysis are defined as the difference between the observed values of Y and the values of Y predicted by the regression equation. The scatterplot or residual plots can be used to see if the regression equation is an appropriate model for the data. An assumption required for the simple linear regression equation to be valid is: the residuals are constant the variance of X is equal to the variance of Y X and Y are independent the variance of the residuals is uniform Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Wednesday, May 25, 2016, 20:12 http://www.perdisco.com.au Introductory Statistics Third Edition Perdisco Assessment Below is a set of assessable homework questions on this topic, selected by your professor. Take care! Do not submit your answers until you have read all the instructions and answered the questions carefully. When you submit your answers, you will receive immediate feedback. Navigating this page: Submit answers: Submit your answers for immediate grading Bookmark: Save this question set so that you can come back to it later 1 of 3 ID: MST.FET.R.SLRM.01.0010A [2 marks] marks] The Vopstra telecommunication company has increased its branding of phones in the stores that sell them. To varying degrees, the shelves that contain Vopstra phones now have advertizing in the form of small posters. Different stores contain different amounts of advertizing, and Vopstra would like to know if there is any relationship between amount spent on advertizing (X) and sales of Vopstra phones (Y). A random sample of 50 stores is selected. For each store, the amount in dollars spent on advertizing and the amount in dollars made in sales of Vopstra phones are recorded. The following regression equation is calculated: ^ y = 75.48 + 3.90x Along with this, the following values were calculated: SSX = 125.80 SST = 299.08 se = 22.92 Vopstra plans on conducting a hypothesis test with 95% confidence and the following hypotheses: H0: 1 = 0 H1: 1 0 You may find this Student's t distribution table useful. a) Calculate the test statistic (t) for this test. Give your answer to 4 decimal places. t= b) The null hypothesis 2 of 3 rejected in this test. ID: MST.FET.R.SLRM.02.0020A [4 marks] marks] A regression model has been developed to analyze the relationship between a response variable Y and an explanatory variable X. A prediction interval is to be constructed for an individual value of Y for a given value of X. Select whether each change would increase, decrease, or not affect the width of the prediction interval. Increase Decrease Not affect a) Decreasing the level of confidence b) Using a larger sample size c) Choosing a value of X further away from x d) Having less variation in the values of the response variable about the prediction line 3 of 3 ID: MST.FET.R.SLRM.03.0040A [2 marks] marks] Given the data listed in the table below, calculate the lower and upper bound of the 99% prediction interval for ^ the response variable at X = 9. The regression equation is given by y = b0 + b1x. Regression Statistics Statistic Value b0 7.8 b1 0.44 x 7.38 se 2.648 SSX 45.27 SST 51.81 n 40 Give your answer to 2 decimal places. You may find this Student's t distribution table useful. a) Lower bound = b) Upper bound = Perdisco / latin /, v., to learn thoroughly 2010 Perdisco Terms Of Use | Privacy Policy | Wednesday, May 25, 2016, 20:13 http://www.perdisco.com.au