00:01
In this question, we're given information about the costs associated with producing certain volumes of a substance.
00:11
So we have a table of values here where x represents the volume that we produce of something and y represents the cost associated with that volume.
00:22
And we want to figure out which of these three statements is not true if we fit this data to a plus bx.
00:32
So in order to do that in desmos, i'm going to say that i want my values in column y1 to be approximated to a plus bx and i want the values in column x1.
00:53
So that gives me the the following here where it tells me that a is about 1321 .32 and b is about 7 .643.
01:05
So let me write this regression out with the numbers here.
01:14
So we have y is equal to 1321 .32 plus 7 .643 approximately multiplied by x.
01:31
So in this case, the value of b is that 7 .643.
01:38
Now in a linear regression, this is in the the slope position.
01:45
So 7 .643 is the slope and the the units of this would be dollars per unit.
01:54
So every unit of volume that we increase that we go up, we're adding 7 .643 dollars to our total cost.
02:03
So this first statement that says the monthly cost will increase by 7 .643 for every one unit increase in volume is completely true.
02:11
So we're looking for the ones that are not true.
02:14
So we can cancel out the first one because we're looking for the incorrect statements.
02:20
The second point it says since b is greater than zero, there is a direct relationship.
02:26
Now a direct relationship means that as we increase one value, the other value also increases or as we decrease one value, the other value also decreases.
02:36
In this case, because we have a regression line, we know that if the value of b is positive, it means we have a positive slope.
02:46
And anytime we have a positive slope, it means increasing x increases y as well...