COMPLETE THE FOLLOWING IN R STUDIO

#1) A study conducted by VPI&SU to determine if certain statistic arm-strength #measures have an influence on the "dynamic lift' characteristic of an #individual. Twenty-five individuals were subjected to strength tests and then #were asked to perform a weight-lifting test in which weight was dynamically #lifted overhead. The data are given here: arm <- c(17.3, 19.3, 19.5, 19.7, 22.9, 23.1, 26.4, 26.8, 27.6, 28.1, 28.2, 28.7,29, 29.6, 29.9, 29.9, 30.3 , 31.3, 36, 39.5, 40.4, 44.3, 44.6, 50.4, 55.9) lift <- c(71.7, 48.3, 88.3, 75, 91.7, 100, 73.3, 65, 75, 88.3, 68.3, 96.7, 76.7, 78.3, 60, 71.7, 85, 85, 88.3, 100, 100, 100, 91.7, 100, 71.7)

#a) How much of the variability in the amount of lift can be explained by the #arm-strength? (correct answer is about 15%)

#b) Does a linear relationship exist? Assume significance level is 0.05.

#2) The grades of a class of 9 students on a midterm report (the predictor) and #on the final examination (the response) are as follows: midterm <- c(77, 50, 71, 72, 81, 94, 96, 99, 67) final <- c(82, 66, 78, 34, 47, 85, 99, 99, 68)

#a) How much of the variability of finals can be explained by midterm grade?

#b) Is there enough evidence to conclude that students who score better on #midterms do better on the final?

#3) A study was made on the amount of converted sugar in a certain process a #various temperatures. The data were coded and recorded as follows: temp <- c(1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0) convert.sugars <- c(8.1, 7.8, 8.5, 9.8, 9.5, 8.9, 8.6, 10.2, 9.3, 9.2, 10.2)

#a) How much variability of converted sugars can be explained by temp? #(correct answer: about 48%)

#b) is there enough evidence to suggest that there is a linear relationship?

#4) A study was made by a retail merchant to determine the relationship between #weekly advertising expenditures and sales. The following data were recorded: ad.cost <- c(40, 20, 25, 20, 30, 50, 40, 20, 50, 40, 25, 50) sales <- c(385, 400, 395, 365, 475, 440, 490, 420, 560, 525, 480, 510)

#a) Plot a scatter plot

#b) Find the equation of the regression line to predict weekly sales from #advertising expenditures

#c)How much of variability of sales can be explained by ad expenditures? #(correct Answer is about 40%)