Model Simple Linear Regression

Linear Regression Author Name Institution Affiliation Question#1 If I am to model the relationship between the mean or expected number of games won by a major-league team and the team’s batting average is x, then a straight line would be used and the slope of a line would be negative. This is because a negative slope line implies that y will decrease when x increases and vice versa. An example of a graph with negative slope is as follows: Negative Slope m =  =  = -  This indicates that when x increases by 3, then y decreases instantly by 4, and when x decreases by 3, then y increases automatically by 4. Question#2 The pattern revealed by the scattergram agrees with my answer to part a. In order to construct a simple linear regression of the data, a linear relationship between the two variables should exist. Whilst there are a couple of ways to determine whether the linear relationship is present between the two variables or not, the best way is to create a scatterplot using SPSS in which the dependent variable can be plotted against the independent variable. The eqaution of least squares line is ŷ= a + b x. Question#3 This graph reveals that the least squares line fits the point on my scattergram. Question#4 After looking at the data, I have found that the mean or expected number of games won is strongly related to a team’s batting average, as the two variables are positively related to one another and their highest values are also interlinked. Question#5 From the regression equation, I have seen that the straight line expression is 119.86 +0.346x. It is a reliable equation as the regression F value is <0.05. In the meantime, the value of  and  are 119.86 and 0.346 respectively. These values have been obtained from the regression table. Question#6 The equation of the least squares line for Brand A and Brand B is as follows: y = mx + b Here, y = how far up m = gradient or slope (how steep the line is) x = how far long b = the Y intercept (the line that crosses the Y axis) Question#7 For the first brand: For the second brand: Question#8 I would like to use the least squares line to predict useful life for a given cutting speed for the second brand, as its value of y is better than the first brand’s value of y. Question#9 The equation of the least squares line is as follows: Question#10 After testing at α = 0.05, I have found that the straight-line model contributes information for predicting overhead costs. Question#11 While a scatterplot allows us to check for autocorrelations, the Correlation matrix is the most effective and best assumption to be made about the random error ϵ in this problem. Whil...