Researchers asked each child in a sample of 411 school-age children if they were more or less likely to purchase a lottery ticket at a store if lottery tickets were visible on the counter. The percentage that said that they were more likely to purchase a ticket by grade level are as follows (R&J Child Development Consultants, Quebec, 2001):

Grade Percentage That Said They
Were More Likely to Purchase

6 32.7
8 46.1
10 75.0
12 83.6

a. Construct a scatterplot of y = percentage who said
they were more likely to purchase and x = grade. Does
there appear to be a linear relationship between x and y?
b. Find the equation of the least-squares line

a) Figure attached

b)

See calculations and explanation below.

Step-by-step explanation:

For this case we have the following data given:

Grade   Percentage That Said They  Were More Likely to Purchase

6                                                   32.7

8                                                   46.1

10                                                 75.0

12                                                 83.6

Part a

We denote:

y = percentage who said  they were more likely to purchase and x = grade

We can construct the scatterplot with Excel.

the result is on the figure attached

Part b

For this case we need to calculate the slope with the following formula:

Where:

So we can find the sums like this:

With these we can find the sums:

And the slope would be:

Nowe we can find the means for x and y like this:

And we can find the intercept using this:

So the line would be given by:

5+2x=a

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