Analyze data to determine whether or not you think there is a relationship between height and ability to lift weights (at least as measured by the bench press). 1- Compute a linear regression line to fit this data, also2- compute the correlation coefficient and coefficient of determination. Answer the following questions:
A) how many more (or fewer) pounds does the typical weight lifter in this sample bench press for each increase of one inch of height. What is the name of the statistic you use to answer this question?
B) What is the predicted weight lifted by a person with a height of zero (0) inches. Why does this silly number (a person with no height) make sense? What is this statistic called?
C) What weight would a person with a height of 60 inches be predicted to lift? What range of variation do you expect in this estimate? (Assume homoscadasticity). What is the name of the statistic you calculated to compute this error range.
D) What proportion of variation in weight lifting ability do you think might be accounted for by a person’s height? What is the name of the statistic that allows you to calculate this?
E) What other factors might account for the variation that cannot be accounted for by the relationship between height and weight lifting ability? How large is this amount?
I am so lost! I have calcualted SSX, SSXY, pearsons R, r^2, Std, error of estimate now what?
Anyone?
still stuck on this...
Great job on calculating SSX, SSXY, Pearson's R, r^2, standard error of estimate! Now let's move on to the next steps.
A) To determine how many more (or fewer) pounds the typical weight lifter in this sample bench presses for each increase of one inch of height, you need to calculate the slope of the linear regression line. The slope represents the rate of change between height and weight lifted. You can use the formula:
slope = SSXY / SSX
Where SSXY is the sum of the cross-products of the differences between each height and weight observation, and SSX is the sum of the squares of the differences between each height observation and its mean. The slope is the statistical measure you can use to answer this question.
B) To predict the weight lifted by a person with a height of zero (0) inches, you need to find the value of the y-intercept of the linear regression line. The y-intercept represents the predicted weight when the height is zero. This value might seem silly since a person with no height may not exist, but it is part of the mathematical model. The y-intercept is referred to as the intercept statistic.
C) To predict the weight lifted by a person with a height of 60 inches, you can substitute the value of 60 into the equation of the linear regression line. The resulting value will be the predicted weight. However, keep in mind that there will be some variation or error in this estimate. To quantify the range of variation, you can use the standard error of estimate. It measures the average distance between each observed weight and its corresponding predicted weight on the regression line.
D) To determine the proportion of variation in weight lifting ability accounted for by a person's height, you can use the coefficient of determination (r^2). It represents the proportion of the total variation in weight lifting ability that can be explained by the linear relationship with height. The higher the r^2 value, the more variation is accounted for by height.
E) Other factors might account for the variation that cannot be explained by the relationship between height and weight lifting ability. These factors could include things like muscle mass, training techniques, genetics, nutrition, and overall fitness level. The amount of variation that cannot be accounted for by the relationship is essentially the remaining proportion of variation (1 - r^2) in weight lifting ability that is not explained by height.
Keep in mind that these statistical measures provide insights into the relationship between height and weight lifting ability but do not necessarily imply causation. It's important to interpret the results in the context of your specific dataset and research question.