TREND

Returns values along a linear trend. Fits a straight line (using the method of least squares) to the arrays known_y's and known_x's. Returns the y-values along that line for the array of new_x's that you specify.

Syntax

TREND(known_y's,known_x's,new_x's,const)

Known_y's   is the set of y-values you already know in the relationship y = mx + b.

• If the array known_y's is in a single column, then each column of known_x's is interpreted as a separate variable.
• If the array known_y's is in a single row, then each row of known_x's is interpreted as a separate variable.

Known_x's   is an optional set of x-values that you may already know in the relationship y = mx + b.

• The array known_x's can include one or more sets of variables. If only one variable is used, known_y's and known_x's can be ranges of any shape, as long as they have equal dimensions. If more than one variable is used, known_y's must be a vector (that is, a range with a height of one row or a width of one column).
• If known_x's is omitted, it is assumed to be the array {1,2,3, ...} that is the same size as known_y's.

New_x's   are new x-values for which you want TREND to return corresponding y-values.

• New_x's must include a column (or row) for each independent variable, just as known_x's does. So, if known_y's is in a single column, known_x's and new_x's must have the same number of columns. If known_y's is in a single row, known_x's and new_x's must have the same number of rows.
• If you omit new_x's, it is assumed to be the same as known_x's.
• If you omit both known_x's and new_x's, they are assumed to be the array {1,2,3, ...} that is the same size as known_y's.

Const   is a logical value specifying whether to force the constant b to equal 0.

• If const is TRUE or omitted, b is calculated normally.
• If const is FALSE, b is set equal to 0 (zero), and the m-values are adjusted so that y = mx.

Remarks

• For information about how Microsoft Excel fits a line to data, see LINEST.
• You can use TREND for polynomial curve fitting by regressing against the same variable raised to different powers. For example, suppose column A contains y-values and column B contains x-values. You can enter x^2 in column C, x^3 in column D, and so on, and then regress columns B through D against column A.
• Formulas that return arrays must be entered as array formulas.
• When entering an array constant for an argument such as known_x's, use commas to separate values in the same row and semicolons to separate rows.

Example

Suppose a business wants to purchase a tract of land in July, the start of the next fiscal year. The business collects cost information that covers the most recent 12 months for a typical tract in the desired area. Known_y values are in cells B2:B13; the known_y values are $133,890, $135,000, $135,790, $137,300, $138,130, $139,100, $139,900, $141,120, $141,890, $143,230, $144,000, $145,290.

When entered as a vertical array in the range C2:C6, the following formula returns the predicted prices for March, April, May, June, and July:

TREND(B2:B13,,{13;14;15;16;17}) equals {146172;147190;148208;149226;150244}

The company can expect a typical tract of land to cost about $150,244 if it waits until July. The preceding formula uses the default array {1;2;3;4;5;6;7;8;9;10;11;12} for the known_x's argument, corresponding to the 12 months of sales data. The array {13;14;15;16;17} corresponds to the next five months.