You can visit the official website of any large restaurant chain to examine the nutritional data for menu items. For fast-food restaurants, many menu items are high in fat, so most of their calorie content comes from fat (rather than carbohydrate or protein). Here we investigate the relationship between amount of fat in a menu item (Fat, measured in grams) and the number of calories ("Calories"). In order to predict the number of calories in a menu item given its fat content, we use the simple linear regression model Caloriesi=?0+?1Fati+ei,i=1,...,nwhere n is the number of observations, and the deviations ei are assumed to be independent and Normally distributed, with mean 0 and standard deviation?. At one major fast-food restaurant chain, there were 26 items listed under the heading of "Sandwiches" (which includes hamburgers, chicken sandwiches, and other sandwich selections) on the menu. We fit the model described above to the data using the method of least squares. The following results were obtained from software.R2 = 0.846S = 43.575Parameter Parameter estimate Std. err. of parameter estb0 151.092 30.082b1 12.546 1.213(a)Suppose the researchers test the hypotheses H0:?1=11 versus Ha:?1

>11

You can visit the official website of any large restaurant chain to examine the nutritional data for menu items. for fast-food restaurants, many menu items are high in fat, so most of their calorie content comes from fat (rather than carbohydrate or protein) . Here we investigate the relationship between amount of fat in a menu item (Fat, measured in grams ) and the number of calories ("Calories"). In order to predict the number of calories in a menu item given its fat content, we use the simple linear regression model Calories; = Bo + Bi Fat; + e, i =1, . .., n where n is the number of observations, and the deviations e, are assumed to be independent and Normally distributed, with mean 0 and standard deviation At one major fast-food restaurant chain, there were 26 items listed under the heading of "Sandwiches" (which includes hamburgers, chicken sandwiches, and other sandwich selections) on the menu. We fit the model described above to the data using the method of least squares. The following results were obtained from software. R- = 0.846 S = 43. 575 Parameter Parameter Std. err. of estimate parameter est bo 151.092 30.082 b1 12.546 1.213 (a ) Suppose the researchers test the hypotheses Ho : B1 = 11 versus Ha : B1 > 11 What is the value of the test statistic for this test? (keep two decimal places) 1.28 A/ (b) What is the statistical decision for the test conducted in part (a) if the level of significance of the test is O = 0.05 (answer either Reject or Not to Reject)(c) Construct a 95$ confidence interval for the mean number of calories when the value of Fat taking the average value of Fat, in the given data set, which is assumed to 100. (Give your solution in an interval format, e.g. (23.45, 45.67) . Make sure that you keep two decimal places and separate two values by comma.) (d) Construct a 95s prediction interval for the predicted number of calories when the value of Fat taking the average value of Fat, in the given data set, which is assumed to 100. (Give your solution in an interval format, e.g. (23.45, 45.67) . Make sure that you keep two decimal places and separate two values by comma.) (e) If the total sum of squares of calories is 1000, what is the value of sum of squares error. (f) What is the estimated coefficient of correlation between Calories and Fat? (keep two decimal places)