Desperate for help with this big regression Qu.

#1
Hello there, I am really struggling with the following question. If you have an idea about how to do any of the parts, I'd be very appreciative of your help! The question is as follows:

"A new device for determining the glucose concentration in human blood samples has been tested against a reference method. Twelve patients provided blood samples whose glucose concentration was then determined by the new device and the reference method. The glucose concentration in mmol/L obtained are given below together with other calculated values.


[ PLEASE SEE ATTACHMENT FOR THE TABLE ]

The sum of cross products of reference and new device result is 1711.87.

(a) Plot the graph of reference result against device result and draw in the line corresponding to equal results from both new device and reference method. What do you conclude about the agreement between the new device and the reference method?

(b) Suppose that, ideally, it would be expected that the new device and the reference method would be linearly related. In using linear regression to estimate that linear relationship which would you take to be 'y' and which would you take to be 'x'? If there was a reason to suppose that the new device and the reference method should give roughly the same values, what values would you expect to see for the slope and the intercept?

(c) Calculate the least squares estimate of the slope and the intercept. What can you conclude from these results about the agreement between the new device and reference method? "

As I say I'm really struggling with this question, so any help would be much appreciated!

Thankyou very much for your time!
 

JohnM

TS Contributor
#2
(a)
make an x-y scatterplot of the data points, then add a line for the equation y=x
visually compare the scatterplot of points to the line --> do they look sort of close?

(b)
x = ref device
y = new device

for the line y=x, it follows the form y = mx + b, where m is the slope and b is the y-intercept

(c)
compute the equation of the best-fit line to the original scatterplot of points in (a) - this equation will give you the slope and intercept of the line that predicts new device readings, based on knowledge of reference device readings (hint: it won't be exactly y=x, but something relatively close)