Question

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. The pair of variables have a significant correlation. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent or a test and their scores on the test are shown below.Hours spend studying, x 1 2 3 3 4 6 (a) x = 2 hours (B) x = 3.5 hrsTest score, y 37 41 51 48 65 69 (c) x = 12 hours (d) x = 1.5 hrsFind the regression equation : Y (hat) = _____x +(_____) round to 3 decimal placesPlot the grapha. predict the value of y for x = 2b. predict the value of y for x = 3.5c. Predict the value of y for x = 12d. predict the value of y for x = 1.5

Answer 1

Answer:

(a)

x = 2

y = 42.019

(b)

x = 3.5

y = 51.833

(c)

x = 12

y = 107.447

(d)

x = 1.5

y = 38.747

Step-by-step explanation:

If you use a regressor calculator you will find that

y = 6.542x + 28.933

then for (a)

x = 2

y = 42.019

(b)

x = 3.5

y = 51.833

(c)

x = 12

y = 107.447

(d)

x = 1.5

y = 38.747

Answer 2

Regression equations are used to represent scatter plots

• The regression equation is $\^y = 6.54\^x + 28.94$
• The predicted values when x = 2, 3.5, 12 and 1.5 are 42.02, 51.83, 107.42 and 38.75

The table is given as:

x | 1 2 3 3 4 6

y | 37 41 51 48 65 69

To determine the regression equation, we make use of an graphing calculator.

From the graphing calculator, we have:

• Sum of X = 21
• Sum of Y = 311
• Mean X = 3.5
• Mean Y = 51.8333
• Sum of squares (SSX) = 17.5
• Sum of products (SP) = 114.5

The regression equation is represented as:

$\^y =b\^x + a$

Where:

$b = \frac{SP}{SS_x}$ and $a = M_y - bM_x$

So, we have:

$b = \frac{SP}{SS_x}$

$b = \frac{17.5}{114.5}$

$b = 6.54$

$a = M_y - bM_x$

$a = 51.83 - (6.54*3.5)$

$a = 28.94$

Substitute values for (a) and (b) in $\^y =b\^x + a$

$\^y = 6.54\^x + 28.94$

The predicted values when x = 2, 3.5, 12 and 1.5 are:

$\^y = 6.54 \times 2 + 28.94 = 42.02$

$\^y = 6.54 \times 3.5 + 28.94 = 51.83$

$\^y = 6.54 \times 12 + 28.94 = 107.42$

$\^y = 6.54 \times 1.5 + 28.94 = 38.75$

Hence, the predicted values when x = 2, 3.5, 12 and 1.5 are 42.02, 51.83, 107.42 and 38.75

Read more about regressions equations at:

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