Question

Finding the Equation of a Regression Line: Find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. If convenient, use technology.

Square Footage and Home Sale Price: The square footages and sale prices (in thousands of dollars) of seven homes are shown in the table below.

1. X = 1450 sq ft.   (b) X = 2720 sq ft. (c) X = 2175 sq ft. (d) X = 1890 sq ft.

X - Sq Ft.	Y - Sale Price
1924	174.9
1592	136.9
2413	275
2332	219.9
1552	120
1312	99.9
1287	145

Answer 1

Sol:

In excel select the data.

Go to

Insert>scatterchart

You will get

CHOLDATA - Excel Sao File Home Insert Page Layout Formulas Data Review View Help Tell me what you want to do 7 Get Add-ins My Add-ins - 5 lo le tu L V E E Illustrations a XX l It Recommended Charts Cha Scatter PivotChart Pivot Table Recommended Table PivotTables Tables 3D Map Slicer Timeline Line Column Win/ Loss Sparklines Add-ins Filters x fc 41 - X-Sq Ft. C A B D E F G L M N X - Sq Ft. Y - Sale Price Scatter Use this chart type to: . Compare at least two sets of values or pairs of data. . Show relationships between sets of values 1924 1592 24131 2332 1552 1312 1287| 174.9 136.9 275 219.9 Use it when: . The data represents separate measurements. 1201 99.9 145

Add axis titles,chart title

Click on one point

add trend line

nart 4 - x fc -SERIES(Sheet3!$B$1,Sheet3!$A$2:$A$8,Sheet3!$B$2:$B$8,1) A B C D E F G H I J K L M 9 300 Y - Sale X - Sq Ft. Price 1924 174.91 1592_ 136.9 2413 275 2332 219.9 1552 120 1312 99.9 1287 145 Series "Y - Sale v 0 Fill Outline il Delete Reset to Match Style Change Series Chart Type... Select Data... 3-D Rotation... 500 1000 3000 0 Add Data Labels Add Trendline...

You get

y = 0.1234x - 51.412 R= 0.8581 Y - Sale Price 500 1000 1500 2000 2500 3000 X - Sq Ft.

Regression eq is

saleprice=0.1234*sqft-51.412

R sq=0.8581

=85.81% variation in sale price is explained by sq ft.

Good model.

when x= 1450 sq ft.

substitute in regression eq

y=0.1234*1450-51.412

y= 127.518

so sale price is 127.518

(b) X = 2720 sq ft

we cannot use this value as it is out of range for which we fit linear regression.

. (c) X = 2175 sq ft

y=0.1234*2175 -51.412

y= 216.983

when sq ft is 2175,sale price is 216.983

. (d) X = 1890 sq ft.

substitute in regression eq we get

y=0.1234*1890 -51.412

y= 181.814

when sq ft is 1890 ,sale price is 181.814