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Chapter 4: Q29P (page 93)

Excel LINEST function. Enter the following data in a spreadsheet and use LINEST to find slope, intercept, and standard errors. Use Excel to draw a graph of the data and add a trendline. Draw error bars of $卤 s_{y}$ on the points.
$\begin{matrix} x : & 3.0 & 10.0 & 20.0 & 30.0 & 40.0 \\ y : & - 0.074 & - 1.411 & - 2.584 & - 3.750 & - 5.407 \end{matrix}$

Short Answer

Expert verified

The slope of the given data is $- 0.13789$

The intercept of the given data is $0.195343$

The standard error of the given data is $0.197625$

The graph of the given data by the use of the LINEST function is given in step 2.

Step by step solution

01

Determine standard deviation of y : sy and the standard uncertainty of the slope and the intercept

The standard deviation ofyis mathematically represented as

$蟽_{y} 鈮� s_{y} = \sqrt{\frac{\underset{}{鈭�} (d_{i}^{2})}{n - 2}}$ .

The standard uncertainty of a slope is mathematically represented as

$u_{m}^{2} = \frac{s_{y}^{2} n}{D}$ .

The standard uncertainty of an intercept is mathematically represented as

$u_{b}^{2} = \frac{s_{y}^{2} \underset{}{鈭�} (x_{i}^{2})}{D}$ .

02

Determine the slope, intercept, and standard errors

The given data is listed below.

Use the Excel LINEST function to calculate the slope, the intercept, and the standard errors.

Use Excel to draw the graph, the error bars of $卤 s_{y}$ on the points.

Excel LINEST function:

The Excel LINEST function used (Figure 1) to calculate the slope, the intercept and the standard errors; and to draw a graph is shown in Figure 2.

From the spreadsheet, the slope is $- 0.13789$ , the intercept is $0.195343$ and the standard error found is $0.197625$

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Most popular questions from this chapter

A trainee in a medical lab will be released to work on her own when her results agree with those of an experienced worker at the 95% confidence level. Results for a blood urea nitrogen analysis are shown below.

Trainee: $\overset{炉}{x} = 14.57 mg / dL s = 0.53 mg / dL n = 6$ samples

Experienced worker: $\overset{炉}{x} = 13.95 mg / dL s = 0.42 mg / dL n = 5$ samples

(a) What does the abbreviation dL stand for?

(b) Should the trainee be released to work alone?

Logarithmic calibration curve. Calibration data spanning five orders of magnitude for an electrochemical determination of p-nitrophenol are given in the table. (The blank has already been subtracted from the measured current.) If you try to plot these dataon a linear graph extending from 0 to $310 渭驳 / mL$ and from 0 to $5260 nA$ , most of the points will be bunched up near the origin. To handle data with such a large range, a logarithmic plot is helpful.

Overwhatrangeisthelog-logcalibrationlinear?

(a) Make a graph of log (current) versus log( concentration). Over what range is the log-log calibration linear?

(b)FindtheequationoftheLine

InTheform $\log (c u r r e n t) = m 脳 \log (c o n c e n t r a t i o n) + b$

(c) Find the concentration of p-nitrophenol corresponding to a signal of 99.9nA.

(d) Propagation of uncertainty with logarithm. For a signal of 99.9nA, log (concentration) and its standard uncertainty turn out to be $0.68315 卤 0.04522$ . With rules for propagation of uncertainty from Chapter 3, find the uncertainty in concentration.

(a) Calculate the fraction of bulbs in Figure 4 - 1 expected to have a lifetime greater than 1005.3h.

(b) What fraction of bulbs is expected to have a lifetime between 798.1 and 901.7h?

(c) Use the Excel NORMDIST function to find the fraction of bulbs expected to have a lifetime between 800and 900h.

Hydrocarbons in the cab of an automobile were measured during trips on the New Jersey Turnpike and trips through the Lincoln Tunnel connecting New York and New Jersey. The concentrations ( $卤$ standard deviations) ofm- andp -xylene were

$Turnpike : 31.4 卤 30.0 渭驳 / m^{3} (32 measurements) Tunnel : 52.9 卤 29.8 渭驳 / m^{3} (32 measurements)$

Do these results differ at the 95%confidence level? At the 99%confidence level?

Use Table 4-1 to state what fraction of a Gaussian population lies within the following intervals:

(a) $渭卤蟽$

(b) $渭卤 2 蟽$

(c) $渭$ to $+ 蟽$

(d) $渭$ to $+ 0.5 蟽$

(e) $- 蟽$ to $- 0.5 蟽$

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