The table below gives the number of hours seven randomly selected students spent studying and their corresponding midterm exam grades.

using this data, consider the equation of the regression line, yˆ = b0 + b1x, for predicting the midterm exam grade that a student will earn based on the number of hours spent studying.

keep in mind, the correlation coefficient may or may not be statistically significant for the data given. remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. hours studying midterm grades1.5 672.5 693 803.5 814 864.5 895.5 94step 1 of 6: find the estimated slope. round your answer to three decimal places. step 2 of 6: find the estimated y-intercept. round your answer to three decimal places. step 3 of 6: determine the value of the dependent variable yˆ at x = 0.step 4 of 6: determine if the statement "not all points predicted by the linear model fall on the same line" is true or false. step 5 of 6: find the estimated value of y when x = 4.5. round your answer to three decimal places. step 6 of 6: find the value of the coefficient of determination. round your answer to three decimal places

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: